Question

Triangle PQR is similar to triangle LMN. Angle Q=113 degrees and angle R=26 degrees what is the measure of angle N

Answer 1

Since triangles PQR and LMN are similar, their corresponding angles are equal.

In triangle PQR:
- Angle Q = 113 degrees
- Angle R = 26 degrees

To find the measure of angle P, we can use the fact that the sum of the angles in a triangle is 180 degrees:

\[
\text{Angle P} = 180^\circ - \text{Angle Q} - \text{Angle R}
\]
\[
\text{Angle P} = 180^\circ - 113^\circ - 26^\circ
\]
\[
\text{Angle P} = 180^\circ - 139^\circ
\]
\[
\text{Angle P} = 41^\circ
\]

Now, since triangles PQR and LMN are similar, we can assume the corresponding relationships for their angles:
- Angle P corresponds to Angle L
- Angle Q corresponds to Angle M
- Angle R corresponds to Angle N

Thus, angle N in triangle LMN corresponds to angle R in triangle PQR:

\[
\text{Angle N} = \text{Angle R} = 26^\circ
\]

Therefore, the measure of angle N is \(26\) degrees.