Triangle ABC is shown with exterior ∠z.
triangle ABC with angle A labeled 77 degrees, angle B labeled 57 degrees, and side AC extended with angle z labeled as exterior angle to angle C
Determine m∠z.
a) 46°
b) 77°
c) 123°
d) 134°
Since the sum of the interior angles of a triangle is 180 degrees, we can find the measure of angle C by subtracting angles A and B from 180 degrees.
m∠C = 180° - 77° - 57° = 46°
The exterior angle ∠z is equal to the sum of the measures of the remote interior angles, which in this case are angles A and C.
m∠z = m∠A + m∠C = 77° + 46° = 123°
Therefore, the measure of ∠z is 123°.
Answer: c) 123°