**3.2.2 Circles II, PT3 Practice**

Question 6:

Question 6:

Diagram below shows a circle with centre

*O*.*POR*is a straight line.Find the value of

*x*and of*y*.

Solution:Solution:

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

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**Question 7:**Diagram below shows a circle with centre

*O*.

Find the value of

*x*.

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

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

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**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}

*x*= exterior angle at

^{2}*Q*

= 180

^{o}– 110

^{o}

= 70

^{o}

*x***= 70**

*y*= reflex angle at

^{o}*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*:$\begin{array}{l}x=95\\ \left(\text{exteriorof}\angle B\text{cyclicquadrilateral}\right)\\ \\ \angle CBF+\angle BFE+{95}^{o}+{110}^{o}={360}^{o}\\ \text{}\angle CBF+\angle BFE+{205}^{o}={360}^{o}\\ \text{}\angle CBF+\angle BFE={155}^{o}\\ \\ {y}^{o}+\angle CBF+\angle BFE={180}^{o}\\ \text{}{y}^{o}+{155}^{o}={180}^{o}\\ \text{}y=25\end{array}$