What is Representing Relationships of Angle Measures

Angles X and Y form a straight line. Angles W and Z form a straight line. Angles X and W are beside each other. Angles Y and Z are beside each other.

Which equation represents the relationship of the measure of m∠X and m∠Y?

m∠X = m∠Y

m∠X + m∠Y = 90°

m∠X + m∠Y = 100°

m∠X + m∠Y = 180°

Given:

Angles X and Y form a straight line. Angles W and Z form a straight line. Angles X and W are beside each other. Angles Y and Z are beside each other.

We need to determine the relationship that represents the measure of ∠X and ∠Y

Option a: m∠X = m∠Y

Two angles are said to be congruent only if they are vertically opposite angles.

Since, we know that the given relationship between X and Y is a straight line, the relationship m∠X = m∠Y does not represent the relationship between X and Y.

Hence, Option a is not the correct answer.

Option b: m∠X + m∠Y = 90°

The given relationship shows that the angles X and Y are complementary angles. Because complementary angles add up to 90°

Hence, the given relationship m∠X + m∠Y = 90° does not represent that the angles X and Y are straight line.

Hence, Option b is not the correct answer.

Option c: m∠X + m∠Y = 100°

The given relationship shows that the sum of the two angles X and Y is 100°

Hence, the relationship m∠X + m∠Y = 90° does not represent that the angles X and Y forms a straight line.

Hence, Option c is not the correct answer.

Option d: m∠X + m∠Y = 180°

The given relationship shows that the angles X and Y are linear pairs of angles. That is, two angles in a straight line add up to 180°

Hence, the relationship m∠X + m∠Y = 90° represents the angles X and Y form a straight line.

Hence, Option d is the correct answer.

The answer is D