Question

Given: Circle O what is the the value of a?

Answer 1

Solution

Recall that:

The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle’s circumference.

That is; Angle XOZ is twice Angle XYZ

Angle XOZ = 48

While angle XYZ = a

$\Rightarrow48=2a$

Dividing both sides by 2

$\begin{gathered} \Rightarrow a=\frac{48}{2} \\ \\ \Rightarrow a=24 \end{gathered}$

Hence, the value of a = 24