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