# 3.2.2 Circles II, PT3 Practice

3.2.2 Circles II, PT3 Practice

Question 5:
Diagram below shows a circle with centre O. POR is a straight line.
Find the value of x and of y.

Solution:
$\begin{array}{l}x=40×2\\ \text{}=80\\ \\ y=\frac{180-80}{2}\\ \text{}=50\end{array}$

Question 6:
Diagram below shows a circle with centre O.

Find the value of x.

Solution:
$\begin{array}{l}\angle QRO={38}^{o},\angle ORS={44}^{o}\\ \angle QRS={38}^{o}+{44}^{o}={82}^{o}\\ {x}^{o}={82}^{o}×2\\ {x}^{o}={164}^{o}\\ x=164\end{array}$

Question 7:
Diagram below shows a circle. QTS is the diameter of the circle and PTR is a straight line.

Find the value of x.

Solution:
$\begin{array}{l}\angle RPS={90}^{o}-{42}^{o}={48}^{o}\\ {x}^{o}={48}^{o}+{37}^{o}={85}^{o}\end{array}$

Question 8:
Diagram below shows a circle with centre O. PQR is a straight line.

Find the value of x and of y.

Solution: