Question

Triangle DEF is similar to XYZ. DEF has angles D, E and F with m <E = 45 and m<F =25. What is m<x?

Answer 1

In similar triangles, corresponding angles are equal. Given triangle DEF with angles \( m \angle E = 45^\circ \) and \( m \angle F = 25^\circ \), we can find the third angle \( m \angle D \).

The sum of the angles in any triangle is \( 180^\circ \):

\[
m \angle D + m \angle E + m \angle F = 180^\circ
\]

Substituting the known angle measures:

\[
m \angle D + 45^\circ + 25^\circ = 180^\circ
\]
\[
m \angle D + 70^\circ = 180^\circ
\]
\[
m \angle D = 180^\circ - 70^\circ = 110^\circ
\]

The angles of triangle DEF are:
- \( m \angle D = 110^\circ \)
- \( m \angle E = 45^\circ \)
- \( m \angle F = 25^\circ \)

Since triangle DEF is similar to triangle XYZ, the corresponding angles will be equal:

- If \( m \angle D \) corresponds to \( m \angle X \), then \( m \angle X = 110^\circ \).
- If \( m \angle E \) corresponds to \( m \angle Y \), then \( m \angle Y = 45^\circ \).
- If \( m \angle F \) corresponds to \( m \angle Z \), then \( m \angle Z = 25^\circ \).

Since the question asks for \( m \angle X \):

\[
m \angle X = 110^\circ
\]

Thus, the answer is:
\[
\boxed{110^\circ}
\]