Given △PQR∼△LMN , m∠Q=113° , and m∠R=26° , what is the measure of angle N ?(1 point)
Since triangles PQR and LMN are similar, we can set up a proportion to find the measure of angle N.
We know that the corresponding angles of similar triangles are equal, so we have:
m∠P/m∠L = m∠Q/m∠M = m∠R/m∠N
In this case, we are given that m∠Q = 113° and m∠R = 26°, so we can set up the proportion:
113°/m∠L = 26°/m∠N
Now we can cross-multiply:
113° * m∠N = 26° * m∠L
To find the measure of angle N, we need the value of m∠L. Unfortunately, the given information does not include the measure of angle L. Therefore, we cannot determine the measure of angle N using the given information.
If △PQR is similar to △LMN, then the corresponding angles are equal. Given that
m
∠
Q
=
11
3
∘
m∠Q=113
∘
and
m
∠
R
=
2
6
∘
m∠R=26
∘
, we can find
m
∠
N
m∠N, which corresponds to
m
∠
Q
m∠Q.
m
∠
N
=
m
∠
Q
m∠N=m∠Q
Therefore,
m
∠
N
=
11
3
∘
m∠N=113
∘
.