Question

The two triangles below are similar.

Also, the measure of angle G = 20° and the measure of angle I = 90°.

Find the measure of angles X, Y, and Z.

Assume the triangles are accurately drawn.

Answer 1

Explanation:

`\mathrm{m \angle I=m \angle X=90^o}\ \mathrm{and \ m \angle Y=m \angle G=20^o} \ \ \mathrm{[Corresponding\ angles\ of}\\\mathrm{similar\ triangles\ are\ equal.]}\\\mathrm{In\ \triangle XYZ,}\\\mathrm{\angle X+\angle Y+\angle Z=180^o\ \ \ [Sum\ of\ angles\ of\ triangle\ is\ 180^o.]}\\\mathrm{or,\ 90^o+20^o+\angle Z=180^o}\\\mathrm{or,\ m\angle Z=70^o}`

Answer 2

Explanation:

angle x = 90 degrees

angle y = 20 degrees

angle z = 70 degrees