Question

Find the value of x.answer choicesA. 70B. 65C. 30D. 40

Answer 1

ANSWER

$70$

EXPLANATION

In the given diagram;

The third angle on the triangle is calculated thus;

Let the third angle of the triangle be y;

$\begin{gathered} y+15+20=180 \\ y=180-(15+20) \\ y=180-35 \\ y=145 \end{gathered}$

Now, the inscribed angle and angle y are on a straight line

Let the inscribed angle be denoted by z, hence;

By sum of angles on a straight line

$\begin{gathered} z+145=180 \\ z=180-145 \\ =35 \end{gathered}$

Recall that intercepted arc is twice of inscribed angle, hence;

$\begin{gathered} x=2z \\ =2\times35 \\ =70 \end{gathered}$