Question

Given triangleABC~triangleDEF
m<A=62 degrees
m<E=13 degrees
what is the measures of angle C?

Answer 1

Since triangles \( ABC \) and \( DEF \) are similar (denoted as \( ABC \sim DEF \)), the corresponding angles are equal. This means:

\[
m<A = m<D, \quad m<B = m<E, \quad m<C = m<F
\]

We are given that \( m<A = 62^\circ \) and \( m<E = 13^\circ \).

Since \( m<B \) corresponds to \( m<E \), we can find \( m<B \):
\[
m<B = m<E = 13^\circ
\]

Now, we can use the fact that the sum of the angles in a triangle is \( 180^\circ \) to find \( m<C \):
\[
m<A + m<B + m<C = 180^\circ
\]
\[
62^\circ + 13^\circ + m<C = 180^\circ
\]

Calculating the left side:
\[
75^\circ + m<C = 180^\circ
\]

Now, solving for \( m<C \):
\[
m<C = 180^\circ - 75^\circ = 105^\circ
\]

Thus, the measure of angle \( C \) is:
\[
\boxed{105^\circ}
\]