Given △PQR∼△LMN, m∠Q=113°, and m∠R=26°, what is the measure of angle N (1 point)
To find the measure of angle N, we can use the fact that corresponding angles in similar triangles are congruent.
Since △PQR∼△LMN, we can write the proportion:
m∠Q / m∠L = m∠R / m∠N
Plugging in the given values:
113° / m∠L = 26° / m∠N
To solve for m∠N, we can cross-multiply and then solve for m∠N:
26° * m∠L = 113° * m∠N
26m∠L = 113m∠N
Divide both sides by 26m∠N:
(26m∠L) / 26m∠N = (113m∠N) / 26m∠N
m∠L / m∠N = 113 / 26
Now, we can substitute the ratio of m∠L and m∠N with the given angle measures:
m∠L / m∠N = 113 / 26
m∠N = (26 * m∠L) / 113
Since m∠L is not given, we cannot determine the exact measure of angle N without additional information about the triangle.
To find the measure of angle N, we need to use the properties of similar triangles. Since △PQR∼△LMN, the corresponding angles of the triangles are equal.
We are given that m∠Q = 113° and m∠R = 26°.
In triangle △PQR, the sum of the angles is always 180°. Therefore, we can find m∠P by subtracting the sum of ∠Q and ∠R from 180°:
m∠P = 180° - (m∠Q + m∠R)
m∠P = 180° - (113° + 26°)
m∠P = 180° - 139°
m∠P = 41°
Since △PQR∼△LMN, the corresponding angles to ∠P and ∠Q in triangle △LMN are equal to ∠N and ∠M, respectively.
Therefore, the measure of angle N is 41°.
it has to be 26
theyre congruent probably so R and N are the same place
R is 26 so?