Question

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 measures of the angles?

x=
y=
z=

Answer 1

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`