Question

Given triangle ABC ~ triangle DEF m~<A = 52° and m<E = 11° what is the measure of angle C

Answer 1

To find the measure of angle C, we can use the property of similar triangles that corresponding angles are congruent.

Since angle A is congruent to angle D, and we know that m<A = 52°, then m<D = 52°.

Similarly, since angle C is congruent to angle F, and we know that m<E = 11°, then m<F = 11°.

Now, we can find the measure of angle C by subtracting the measures of angles A and B from 180° (since the sum of the angles in a triangle is always 180°).

m<C = 180° - (m<A + m<B)
m<C = 180° - (52° + 11°)
m<C = 180° - 63°
m<C = 117°

Therefore, the measure of angle C is 117°.