Q:

Geometry In triangle XYZ the measure of angle X is eight times the sum of themeasures of angles Y and 2 The measure of angle Y is three times themeasure of angle 2 What are the measures of the angles?

Accepted Solution

A:
Answer:The measures of the angles are: x=160°, y=15°, and z=5° Step-by-step explanation:Consider the provided information.The measure of angle X is eight times the sum of the  measures of angles Y and 2This can be written as:x=8(y+z)The measure of angle Y is three times the  measure of angle z.y=3(z)Substitute the value of y in x=8(y+z).x=8(3z+z)x=32zAs we know the sum of interior angles of a triangle is 180°x+y+z=180°Substitute the value of x and y in above equation,32z+3z+z=180°36z=180°z=5°The measure of angle Y is:y=3(5°)y=15°Substitute the value of z=5° in x=32zx=32(5°)x=160°Hence, the measures of the angles are: x=160°, y=15°, and z=5°