In a diagram, ∠X and ∠Y are vertical angles and ∠Y is a complementary angle with ∠Z. If m∠X is 77°, write an equation that you can use for m∠Z
Since ∠X and ∠Y are vertical angles, this means that they are congruent. Therefore, m∠X = m∠Y = 77°.
We are also given that ∠Y is a complementary angle with ∠Z. We know that the sum of two complementary angles is 90°. Therefore, m∠Y + m∠Z = 90°.
Substituting m∠Y = 77° into the equation, we get:
77° + m∠Z = 90°
So the equation that can be used for m∠Z is 77° + m∠Z = 90°.