Question

Find the value of x. Write your answer as a decimal.

Answer 1

ANSWER

$x = 75.5 \degree$

EXPLANATION

Lines WO and WX are tangents to the circle.

The angle subtended at the center, Z by minor arc XO is the angle subtended at the circumcenter by the same arc.

Therefore the central angle is 2x°.

The two radii ZX and ZO meets the tangents at right angles.

This implies that:

$2x + 90 + 90 + 29 = 360 \degree$

Or

$2x + 29 = 180 \degree$

$2x = 180 - 29$

$2x = 151$

Divide both sides by 2

$x = \frac{151}{2} = 75.5$