A triangle has three interior angle measures; x is the largest angle, y is the next largest angle, and z is the smallest angle. The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles. The largest angle is twice the smaller angle plus 20 degrees. The sum of the triangle's interior angles is x + y + z = 180. Which two equations represent the remaining angle relationships? Select each correct answer.

x = 2z + 20
x=2(z+y)−60
x=2z+y−60
x = z + 20
x=60−2(z+y)

The two equations that represent the remaining angle relationships are (x = 60 - 2(y + z)) and (x = 2z + 20) and this can be determined by using the given data.

Given :

A triangle has three interior angle measures; x is the largest angle, y is the next largest angle, and z is the smallest angle.
The measure of the largest angle is 60 degrees less than twice the sum of the measure of the other two angles.
The largest angle is twice the smaller angle plus 20 degrees.
The sum of the triangle's interior angles is x + y + z = 180.

The linear equation that represents the situation "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles" is:

x = 60 - 2(y + z) --- (1)

The linear equation that represents the situation "The largest angle is twice the smaller angle plus 20 degrees" is:

x = 2z + 20 --- (2)

Therefore, the correct option is A) and E).

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