Given:
m∠XYZ = 72 degrees
m∠XYZ and m∠ZYC form a linear pair.
Let's find the measure of ∠ZYC.
To find the measure of angle ZYC, apply the Linear Pair of Angles theorem which states that the sum of angles that form a linear pair is 180 degrees.
Hence, we have:
m∠XYZ + m∠ZYC = 180
72 + m∠ZYC = 180
• Subtract 72 from both sides:
72 - 72 + m∠ZYC = 180 - 72
m∠ZYC = 180 - 72
m∠ZYC = 108 degrees.
Therefore, the measure of ∠ZYC is 108 degrees.
ANSWER:
C. 108°
