Calculate the size of:
- \(p\)
- \(R\hat{K}U\)
- \[\begin{align} 2p-55°+3p+70° &=180° &(\angle\text{s on a straight line}) \\ 5p+125°&=180° \\ 5p&=55° \\ p&=11° \end{align}\]
- \[R\hat{K}U = 3p =3(11^{\circ})=33^{\circ}\]
12.8 End of chapter exercises
Exercise 12.8
Calculate the size of \( y \)
\[\begin{align}
102°-2y &=78° & (\text{vert opp }\angle\text{s}) \\
-2y &=78°-102° \\
-2y &=-24° \\
y &= 12°
\end{align}\]
Calculate the size of \( r \)
\[\begin{align}
180°-3r &=126° & (\text{vert opp }\angle\text{s}) \\
-3r &=126° - 180° \\
-3r &=-54° \\
r &=18°
\end{align}\]
Find the sizes of all the angles \(\hat{1}\) to \(\hat{7}\).
\[\begin{align}
\hat{1} &= 180°-154°&&(\angle\text{s on a straight line}) \\
\hat{1} &= 26° \\
\hat{2}&=154°&& (\text{vert opp }\angle\text{s}) \\
\hat{3}&=26°&& (\text{vert opp }\angle\text{s}) \\
\hat{4} &=\hat{1} &&(\text{corresp }\angle\text{s}; XY \parallel ZW) \\
\hat{4} &= 26° \\
\hat{5} &=154 °&&(\text{corresp }\angle\text{s}; XY \parallel ZW) \\
\hat{6}&=154°&& (\text{vert opp }\angle\text{s}) \\
\hat{7}&=26°&& (\text{vert opp }\angle\text{s}) \\
\end{align}\]
In the diagram, \(OK = ON\), \(KN \parallel LM\), \(KL \parallel MN\) and \(\hat{LKO}=160^{\circ}\). Calculate the value of \(x\). Give reasons for your answers.
\[\begin{align}
\hat{LKN} &=140° &&(\text{opp }\angle\text{s} \text{ of parallelogram = )} \\
\hat{OKN} &=160°-140° \\
\hat{OKN} &=20° \\
\hat{ONK} &=20° &&(\angle\text{s opp = sides}) \\
\hat{ONK}+ \hat{OKN}+ x &=180°&&(\text{sum of }\angle\text{s in } \triangle ) \\
20°+ 20° +x &=180° \\
x&=180° -20°-20° \\
x&=140° \\
\end{align}\]