<u>Given</u>:
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
<u>Option a</u>: 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.
<u>Option b</u>: 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.
<u>Option c</u>: 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.
<u>Option d</u>: 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.
.
