Question

108°
N
z = [? ]°
y
W
40°

Answer 1

z = 20°

Explanation:

You want the measure of inscribed angle z that intercepts an arc of 40°.

Inscribed angle

The measure of an inscribed angle is half the measure of the arc it intercepts:

z = 40°/2

z = 20°

__

Additional comment

Inscribed angles that intercept the same arc have the same measure:

x = z = 20°

The other angles in the figure are ...

w = y = 108°/2 = 54°

This means the two triangles are similar, and the measure of their third interior angle is 180° -20° -54° = 106°.

<95141404393>