2. Measuring angles

Diagrams of acute, obtuse and reflex angles are below.

These are LaTeX generated only with the answer sheet first followed by the question sheet in the pdfs.

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2.1. Question page

A sample question page file is shown below.

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2.2. Answer page

A sample answer page file is shown below.

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2.3. Tex and pdf files

A 2 page worksheet for acute angles:

measuring_angles_acute_ws2.tex

measuring_angles_acute_ws2.pdf

A 2 page worksheet for obtuse angles:

measuring_angles_obtuse_ws2.tex

measuring_angles_obtuse_ws2.pdf

A 2 page worksheet for reflex angles:

measuring_angles_reflex_ws2.tex

measuring_angles_reflex_ws2.pdf

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2.4. Acute angles

The .tex file to regenerate random acute angles is shown below.

\documentclass{article}
\usepackage{tikz}
\usepackage{multicol}
\usepackage{fancyhdr}
% Underlining package
\usepackage{ulem}
\usepackage[a4paper, portrait, margin=1cm]{geometry}

\def \HeadingAnswers {\section*{\Large Name: \underline{\hspace{8cm}} \hfill Date: \underline{\hspace{3cm}}} \vspace{-3mm}
{Acute angles: Answers} \vspace{1pt}\hrule}
\def \HeadingQuestions {\section*{\Large Name: \underline{\hspace{8cm}} \hfill Date: \underline{\hspace{3cm}}} \vspace{-3mm}
{Acute angles: Questions} \vspace{1pt}\hrule}

% raise footer with page number; no header
\fancypagestyle{myfancypagestyle}{
  \fancyhf{}% clear all header and footer fields
  \renewcommand{\headrulewidth}{0pt} % no rule under header
  \fancyfoot[C] {\thepage} \setlength{\footskip}{14.5pt} % raise page number allowed min 14.5pt
}
\pagestyle{myfancypagestyle}  % apply myfancypagestyle

\pgfmathsetmacro{\arm}{6}
\pgfmathsetmacro{\minAngle}{20}
\pgfmathsetmacro{\maxAngle}{85}
\pgfmathsetmacro{\minAngleAB}{0}
\pgfmathsetmacro{\maxAngleAB}{85}
% \pgfmathsetmacro{\coldiag}{3}
\pgfmathsetmacro{\maxdiag}{12}

\begin{document}
\HeadingAnswers
\vspace{1mm}
\begin{multicols}{2}
\def\AngleList{}
\def\AngleABList{}
\foreach \x in {1,...,\maxdiag} {
    \pgfmathsetmacro{\Angle}{random(\minAngle,\maxAngle)}
    \pgfmathsetmacro{\AngleAB}{random(\minAngleAB,\maxAngleAB)}
    % the first item in the array is blank, then items 1 to 10 are stored
    \xdef\AngleList{\AngleList,\Angle}
    \xdef\AngleABList{\AngleABList,\AngleAB}

    \pgfmathsetmacro{\xA}{\arm *cos(\AngleAB)}
    \pgfmathsetmacro{\yA}{\arm *sin(\AngleAB)}
    \pgfmathsetmacro{\xC}{\arm *cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\yC}{\arm *sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\ABClabelX}{0.5*cos(\AngleAB)}
    \pgfmathsetmacro{\ABClabelY}{0.5*sin(\AngleAB) - 0.3}
    \pgfmathsetmacro{\xarcAB}{1*cos(\AngleAB)}
    \pgfmathsetmacro{\yarcAB}{1*sin(\AngleAB)}
    \pgfmathsetmacro{\AlabelX}{\xA + 0.2*cos(\AngleAB)}
    \pgfmathsetmacro{\AlabelY}{\yA + 0.2*sin(\AngleAB)}
    \pgfmathsetmacro{\ClabelX}{\xC + 0.2*cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\ClabelY}{\yC + 0.2*sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\BlabelX}{-0.2*cos(\Angle/2 + \AngleAB)}
    \pgfmathsetmacro{\BlabelY}{-0.2*sin(\Angle/2  + \AngleAB)}

    \begin{minipage}[t]{0.1\linewidth}
    Q \x)
    \end{minipage}
    \hspace{0.1cm}
    \begin{minipage}[]{0.8\linewidth}
    \begin{tikzpicture}
    \coordinate (A) at (0,0);
    \coordinate (B) at (\xA,\yA);
    \coordinate (C) at (\xC,\yC);
    \draw (A) -- (B) -- cycle;
    \draw (A) -- (C) -- cycle;
    \draw[-] (\xarcAB,\yarcAB) arc [start angle=\AngleAB, end angle=\Angle + \AngleAB, radius=1cm];
    \node[right] at (\ABClabelX,\ABClabelY) {\raggedright $\theta = \Angle^\circ$};
    \node[] at (\BlabelX,\BlabelY) {B};
    \node[] at (\AlabelX,\AlabelY) {A};
    \node[] at (\ClabelX,\ClabelY) {C};
    \end{tikzpicture}
    \end{minipage}
    \vspace{1cm}
    % \ifnum\x=\coldiag
    %     \vfill\null
    %     \columnbreak
    % \fi
}
\end{multicols}

\cleardoublepage
\setcounter{page}{1}

\newpage
\HeadingQuestions
\vspace{1mm}
\begin{multicols}{2}
% Iterate over the values in the angleList array
\foreach \x in {1,...,\maxdiag} {
    \pgfmathsetmacro{\Angle}{{\AngleList}[\x]}
    \pgfmathsetmacro{\AngleAB}{{\AngleABList}[\x]}
    \pgfmathsetmacro{\xA}{\arm *cos(\AngleAB)}
    \pgfmathsetmacro{\yA}{\arm *sin(\AngleAB)}
    \pgfmathsetmacro{\xC}{\arm *cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\yC}{\arm *sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\ABClabelX}{0.5*cos(\AngleAB)}
    \pgfmathsetmacro{\ABClabelY}{0.5*sin(\AngleAB) - 0.3}
    \pgfmathsetmacro{\xarcAB}{1*cos(\AngleAB)}
    \pgfmathsetmacro{\yarcAB}{1*sin(\AngleAB)}
    \pgfmathsetmacro{\AlabelX}{\xA + 0.2*cos(\AngleAB)}
    \pgfmathsetmacro{\AlabelY}{\yA + 0.2*sin(\AngleAB)}
    \pgfmathsetmacro{\ClabelX}{\xC + 0.2*cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\ClabelY}{\yC + 0.2*sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\BlabelX}{-0.2*cos(\Angle/2 + \AngleAB)}
    \pgfmathsetmacro{\BlabelY}{-0.2*sin(\Angle/2  + \AngleAB)}

    \begin{minipage}[t]{0.1\linewidth}
    Q \x)
    \end{minipage}
    \hspace{0.1cm}
    \begin{minipage}[]{0.8\linewidth}
    \begin{tikzpicture}
    \coordinate (A) at (0,0);
    \coordinate (B) at (\xA,\yA);
    \coordinate (C) at (\xC,\yC);
    \draw (A) -- (B) -- cycle;
    \draw (A) -- (C) -- cycle;
    \draw[-] (\xarcAB,\yarcAB) arc [start angle=\AngleAB, end angle=\Angle + \AngleAB, radius=1cm];
    \node[right] at (\ABClabelX,\ABClabelY) {\raggedright $\theta = \dotuline{~~~~~~~}$};
    \node[] at (\BlabelX,\BlabelY) {B};
    \node[] at (\AlabelX,\AlabelY) {A};
    \node[] at (\ClabelX,\ClabelY) {C};
    \end{tikzpicture}
    \end{minipage}
    \vspace{1cm}
    % \ifnum\x=\coldiag
    %     \vfill\null
    %     \columnbreak
    % \fi
}
\end{multicols}

\end{document}

---

2.5. Obtuse angles

The .tex file to regenerate random obtuse angles is shown below.

\documentclass{article}
\usepackage{tikz}
\usepackage{multicol}
\usepackage{fancyhdr}
% Underlining package
\usepackage{ulem}
\usepackage[a4paper, portrait, margin=1cm]{geometry}

\def \HeadingAnswers {\section*{\Large Name: \underline{\hspace{8cm}} \hfill Date: \underline{\hspace{3cm}}} \vspace{-3mm}
{Obtuse angles: Answers} \vspace{1pt}\hrule}
\def \HeadingQuestions {\section*{\Large Name: \underline{\hspace{8cm}} \hfill Date: \underline{\hspace{3cm}}} \vspace{-3mm}
{Obtuse angles: Questions} \vspace{1pt}\hrule}

% raise footer with page number; no header
\fancypagestyle{myfancypagestyle}{
  \fancyhf{}% clear all header and footer fields
  \renewcommand{\headrulewidth}{0pt} % no rule under header
  \fancyfoot[C] {\thepage} \setlength{\footskip}{14.5pt} % raise page number allowed min 14.5pt
}
\pagestyle{myfancypagestyle}  % apply myfancypagestyle

\pgfmathsetmacro{\arm}{6}
\pgfmathsetmacro{\minAngle}{95}
\pgfmathsetmacro{\maxAngle}{180}
\pgfmathsetmacro{\minAngleAB}{0}
\pgfmathsetmacro{\maxAngleAB}{30}

\pgfmathsetmacro{\maxdiag}{8}

\begin{document}
\HeadingAnswers
\vspace{1mm}
\def\AngleList{}
\def\AngleABList{}
\foreach \x in {1,...,\maxdiag} {
    \pgfmathsetmacro{\Angle}{random(\minAngle,\maxAngle)}
    \pgfmathsetmacro{\AngleAB}{random(\minAngleAB,\maxAngleAB)}
    % the first item in the array is blank, then items 1 to 10 are stored
    \xdef\AngleList{\AngleList,\Angle}
    \xdef\AngleABList{\AngleABList,\AngleAB}

    \pgfmathsetmacro{\xB}{\arm *cos(\AngleAB)}
    \pgfmathsetmacro{\yB}{\arm *sin(\AngleAB)}
    \pgfmathsetmacro{\xC}{\arm *cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\yC}{\arm *sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\BAClabelX}{0.5*cos(\AngleAB)}
    \pgfmathsetmacro{\BAClabelY}{0.5*sin(\AngleAB) - 0.3}
    \pgfmathsetmacro{\xarcB}{1*cos(\AngleAB)}
    \pgfmathsetmacro{\yarcB}{1*sin(\AngleAB)}
    \pgfmathsetmacro{\BlabelX}{\xB + 0.2*cos(\AngleAB)}
    \pgfmathsetmacro{\BlabelY}{\yB + 0.2*sin(\AngleAB)}
    \pgfmathsetmacro{\ClabelX}{\xC + 0.2*cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\ClabelY}{\yC + 0.2*sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\AlabelX}{-0.2*cos(\Angle/2 + \AngleAB)}
    \pgfmathsetmacro{\AlabelY}{-0.2*sin(\Angle/2  + \AngleAB)}

    \begin{minipage}[t]{0.1\linewidth}
    Q \x)
    \end{minipage}
    \hspace{0.2cm}
    \begin{minipage}[]{0.8\linewidth}
    \begin{tikzpicture}
    \coordinate (A) at (0,0);
    \coordinate (B) at (\xB,\yB);
    \coordinate (C) at (\xC,\yC);
    \draw (A) -- (B) -- cycle;
    \draw (A) -- (C) -- cycle;
    \draw[-] (\xarcB,\yarcB) arc [start angle=\AngleAB, end angle=\Angle + \AngleAB, radius=1cm];
    \node[right] at (\BAClabelX,\BAClabelY) {\raggedright $\theta = \Angle^\circ$};
    \node[] at (\AlabelX,\AlabelY) {A};
    \node[] at (\BlabelX,\BlabelY) {B};
    \node[] at (\ClabelX,\ClabelY) {C};
    \end{tikzpicture}
    \end{minipage}
    \vspace{1cm}
}

\cleardoublepage
\setcounter{page}{1}

\newpage
\HeadingQuestions
\vspace{1mm}
% Iterate over the values in the angleList array
\foreach \x in {1,...,\maxdiag} {
    \pgfmathsetmacro{\Angle}{{\AngleList}[\x]}
    \pgfmathsetmacro{\AngleAB}{{\AngleABList}[\x]}
    \pgfmathsetmacro{\xB}{\arm *cos(\AngleAB)}
    \pgfmathsetmacro{\yB}{\arm *sin(\AngleAB)}
    \pgfmathsetmacro{\xC}{\arm *cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\yC}{\arm *sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\BAClabelX}{0.5*cos(\AngleAB)}
    \pgfmathsetmacro{\BAClabelY}{0.5*sin(\AngleAB) - 0.3}
    \pgfmathsetmacro{\xarcB}{1*cos(\AngleAB)}
    \pgfmathsetmacro{\yarcB}{1*sin(\AngleAB)}
    \pgfmathsetmacro{\BlabelX}{\xB + 0.2*cos(\AngleAB)}
    \pgfmathsetmacro{\BlabelY}{\yB + 0.2*sin(\AngleAB)}
    \pgfmathsetmacro{\ClabelX}{\xC + 0.2*cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\ClabelY}{\yC + 0.2*sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\AlabelX}{-0.2*cos(\Angle/2 + \AngleAB)}
    \pgfmathsetmacro{\AlabelY}{-0.2*sin(\Angle/2  + \AngleAB)}

    \begin{minipage}[t]{0.1\linewidth}
    Q \x)
    \end{minipage}
    \hspace{0.2cm}
    \begin{minipage}[]{0.8\linewidth}
    \begin{tikzpicture}
    \coordinate (A) at (0,0);
    \coordinate (B) at (\xB,\yB);
    \coordinate (C) at (\xC,\yC);
    \draw (A) -- (B) -- cycle;
    \draw (A) -- (C) -- cycle;
    \draw[-] (\xarcB,\yarcB) arc [start angle=\AngleAB, end angle=\Angle + \AngleAB, radius=1cm];
    \node[right] at (\BAClabelX,\BAClabelY) {\raggedright $\theta = \dotuline{~~~~~~~}$};
    \node[] at (\AlabelX,\AlabelY) {A};
    \node[] at (\BlabelX,\BlabelY) {B};
    \node[] at (\ClabelX,\ClabelY) {C};
    \end{tikzpicture}
    \end{minipage}
    \vspace{1cm}
}


\end{document}

---

2.6. Reflex angles

The .tex file to regenerate random reflex angles is shown below.

\documentclass{article}
\usepackage{tikz}
\usepackage{multicol}
\usepackage{fancyhdr}
% Underlining package
\usepackage{ulem}
\usepackage[a4paper, portrait, margin=1cm]{geometry}

\def \HeadingAnswers {\section*{\Large Name: \underline{\hspace{8cm}} \hfill Date: \underline{\hspace{3cm}}} \vspace{-3mm}
{Reflex angles: Answers} \vspace{1pt}\hrule}
\def \HeadingQuestions {\section*{\Large Name: \underline{\hspace{8cm}} \hfill Date: \underline{\hspace{3cm}}} \vspace{-3mm}
{Reflex angles: Questions} \vspace{1pt}\hrule}

% raise footer with page number; no header
\fancypagestyle{myfancypagestyle}{
  \fancyhf{}% clear all header and footer fields
  \renewcommand{\headrulewidth}{0pt} % no rule under header
  \fancyfoot[C] {\thepage} \setlength{\footskip}{14.5pt} % raise page number allowed min 14.5pt
}
\pagestyle{myfancypagestyle}  % apply myfancypagestyle

\pgfmathsetmacro{\arm}{6}
\pgfmathsetmacro{\minAngle}{270}
\pgfmathsetmacro{\maxAngle}{350}
\pgfmathsetmacro{\minAngleAB}{0}
\pgfmathsetmacro{\maxAngleAB}{180}

\pgfmathsetmacro{\maxdiag}{6}

\begin{document}
\HeadingAnswers
\vspace{1mm}
\def\AngleList{}
\def\AngleABList{}
\foreach \x in {1,...,\maxdiag} {
    \pgfmathsetmacro{\Angle}{random(\minAngle,\maxAngle)}
    \pgfmathsetmacro{\AngleAB}{random(\minAngleAB,\maxAngleAB)}
    % the first item in the array is blank, then items 1 to 10 are stored
    \xdef\AngleList{\AngleList,\Angle}
    \xdef\AngleABList{\AngleABList,\AngleAB}

    \pgfmathsetmacro{\xB}{\arm *cos(\AngleAB)}
    \pgfmathsetmacro{\yB}{\arm *sin(\AngleAB)}
    \pgfmathsetmacro{\xC}{\arm *cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\yC}{\arm *sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\BAClabelX}{-.5*cos(\AngleAB)-3}
    \pgfmathsetmacro{\BAClabelY}{-.5*sin(\AngleAB)-0.1}
    \pgfmathsetmacro{\xarcB}{1*cos(\AngleAB)}
    \pgfmathsetmacro{\yarcB}{1*sin(\AngleAB)}
    \pgfmathsetmacro{\BlabelX}{\xB + 0.2*cos(\AngleAB)}
    \pgfmathsetmacro{\BlabelY}{\yB + 0.2*sin(\AngleAB)}
    \pgfmathsetmacro{\ClabelX}{\xC + 0.2*cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\ClabelY}{\yC + 0.2*sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\AlabelX}{0.2*cos(\Angle/2 + \AngleAB)}
    \pgfmathsetmacro{\AlabelY}{0.2*sin(\Angle/2  + \AngleAB)}

    \begin{minipage}[t]{0.1\linewidth}
    Q \x)
    \end{minipage}
    \hspace{0.2cm}
    \begin{minipage}[]{0.8\linewidth}
    \begin{tikzpicture}
    \coordinate (A) at (0,0);
    \coordinate (B) at (\xB,\yB);
    \coordinate (C) at (\xC,\yC);
    \draw (A) -- (B) -- cycle;
    \draw (A) -- (C) -- cycle;
    \draw[-] (\xarcB,\yarcB) arc [start angle=\AngleAB, end angle=\Angle + \AngleAB, radius=1cm];
    \node[right] at (\BAClabelX,\BAClabelY) {\raggedright $\theta = \Angle^\circ$};
    \node[] at (\AlabelX,\AlabelY) {A};
    \node[] at (\BlabelX,\BlabelY) {B};
    \node[] at (\ClabelX,\ClabelY) {C};
    \end{tikzpicture}
    \end{minipage}
    \vspace{1cm}
}

\cleardoublepage
\setcounter{page}{1}

\newpage
\HeadingQuestions
\vspace{1mm}
% Iterate over the values in the angleList array
\foreach \x in {1,...,\maxdiag} {
    \pgfmathsetmacro{\Angle}{{\AngleList}[\x]}
    \pgfmathsetmacro{\AngleAB}{{\AngleABList}[\x]}
    \pgfmathsetmacro{\xB}{\arm *cos(\AngleAB)}
    \pgfmathsetmacro{\yB}{\arm *sin(\AngleAB)}
    \pgfmathsetmacro{\xC}{\arm *cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\yC}{\arm *sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\BAClabelX}{-.5*cos(\AngleAB)-3}
    \pgfmathsetmacro{\BAClabelY}{-.5*sin(\AngleAB)-0.1}
    \pgfmathsetmacro{\xarcB}{1*cos(\AngleAB)}
    \pgfmathsetmacro{\yarcB}{1*sin(\AngleAB)}
    \pgfmathsetmacro{\BlabelX}{\xB + 0.2*cos(\AngleAB)}
    \pgfmathsetmacro{\BlabelY}{\yB + 0.2*sin(\AngleAB)}
    \pgfmathsetmacro{\ClabelX}{\xC + 0.2*cos(\Angle + \AngleAB)}
    \pgfmathsetmacro{\ClabelY}{\yC + 0.2*sin(\Angle + \AngleAB)}
    \pgfmathsetmacro{\AlabelX}{0.2*cos(\Angle/2 + \AngleAB)}
    \pgfmathsetmacro{\AlabelY}{0.2*sin(\Angle/2  + \AngleAB)}

    \begin{minipage}[t]{0.1\linewidth}
    Q \x)
    \end{minipage}
    \hspace{0.2cm}
    \begin{minipage}[]{0.8\linewidth}
    \begin{tikzpicture}
    \coordinate (A) at (0,0);
    \coordinate (B) at (\xB,\yB);
    \coordinate (C) at (\xC,\yC);
    \draw (A) -- (B) -- cycle;
    \draw (A) -- (C) -- cycle;
    \draw[-] (\xarcB,\yarcB) arc [start angle=\AngleAB, end angle=\Angle + \AngleAB, radius=1cm];
    \node[right] at (\BAClabelX,\BAClabelY) {\raggedright $\theta = \dotuline{~~~~~~~}$};
    \node[] at (\AlabelX,\AlabelY) {A};
    \node[] at (\BlabelX,\BlabelY) {B};
    \node[] at (\ClabelX,\ClabelY) {C};
    \end{tikzpicture}
    \end{minipage}
    \vspace{1cm}
}


\end{document}