Given △PQR∼△LMN , m∠Q=113° , and m∠R=26° , what is the measure of angle N ?

Answer 1

To find the measure of angle N in triangle LMN, we need to use the properties of similar triangles.

From the given information, we know that angle Q in triangle PQR corresponds to angle L in triangle LMN, and angle R in triangle PQR corresponds to angle M in triangle LMN.

Therefore, we can set up the following proportion:

m∠Q/m∠L = m∠R/m∠M

113/x = 26/∠N

Cross multiplying, we get:

26x = 113*∠N

26x = 113∠N

Dividing by 26:

x = 113/26

x = 4.34

Therefore, the measure of angle N in triangle LMN is approximately 4.34 degrees.