Question

What is the value of x?

Answer 1

ANSWER

58°

EXPLANATION

The relationship between the measure of the bigger arc and the smaller arc and the angle created by the secant and the tangent is

$51 \degree = \frac{1}{2} (160 - x)$

Multiply through by 2

This implies that

$2 \times 51 \degree =2 \times \frac{1}{2} (160 - x)$

We simplify to get:

$102 \degree =160 - x$

Solve for x.

$102 \degree - 160 \degree =- x$

$- 58 \degree =- x$

$58 \degree =x$