6.6.3 Angles and Tangents of Circles, PT3 Practice

Question 7:
Diagram below shows a circle with centre O.

Find the value of x.

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

Question 8:
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 9:
Diagram below shows a circle with centre O. PQR is a straight line.

Find the value of x and of y.

Solution:
In cyclic quadrilateral,
Angle at Q = 180^o – 70^o = 110^o
x² = exterior angle at Q
= 180^o – 110^o
= 70^o
x = 70

y^o = reflex angle at O
y^o = 360^o – (70^o × 2)
y^o = 220^o
y = 220

Question 10:
In diagram below, ABCD and DEFG are straight lines.
Find the value of x and of y.

Solution:
$\begin{array}{l}x=95\\ \left(\text{exterior of }\angle B\text{ cyclic quadrilateral}\right)\\ \\ \angle CBF+\angle BFE+{95}^o+{110}^o={360}^o\\ \angle CBF+\angle BFE+{205}^o={360}^o\\ \angle CBF+\angle BFE={155}^o\\ \\ y^o+\angle CBF+\angle BFE={180}^o\\ y^o+{155}^o={180}^o\\ y=25\end{array}$