Question

1. Solve for x= 35, 103

Answer 1

Given:

A figure of a circle with secants intersecting inside the circle.

To find:

The value of x.

Solution:

According to the intersection theorem of secants, if two secants intersect each other inside the circle, then the angle on the intersection is the average of the intercepted arcs.

Using the intersection theorem of secants, we get

$x^\circ=\dfrac{1}{2}(35^\circ+103^\circ)$

$x^\circ=\dfrac{1}{2}(138^\circ)$

$x^\circ=69^\circ$

$x=69$

Therefore, the value of x is 69.