In triangle ABC, the measure of angle X is eight times the sum of the measures of angles Y and Z. The measure of angle Y is three times the measure of angle Z. What are the meas…

Question

asked Dec 23, 2020 2.7k views

1 Answer

Qfd · Answer 1 · 2020-12-27T21:30:32+0000

Answer:

Explanation:

We know that the sum of the angles in a triangle is equal to 180, so we can set up the following equation:

X + Y + Z = 180

From the problem statement, we can also set up the following two equations:

X = 8(Y + Z)

Y = 3Z

Substituting the last equation into the second, we get the following:

X = 8(3Z + Z)

X = 8(4Z)

X = 32Z

Substituting the last two equations into the first, we get the following:

32Z + 3Z + Z = 180

36Z = 180

Z = 5

We can then plug this number into the previous equations:

Y = 3Z

Y = 15

and

X = 32Z

X = 160