Use the image to answer the question. An illustration shows two right triangles with congruent corresponding angles. Triangle A B C is larger than triangle S R T. In triangle A B C, angle A measures 90 degrees, angle B does not have a measurement, and angle C measures 34 degrees. In triangle S R T, angle S measures 90 degrees, angle R measures 56 degrees, and angle T measures 34 degrees.If △ABC∼△SRT , what is m∠B ?(1 point)m∠B =°
Since the triangles are similar and correspondingly congruent, we can conclude that angle B is congruent to angle R. Therefore, m∠B = m∠R = 56 degrees.
△LMN is isosceles, with ∠M≅∠L and m∠L=36° . What are the measures of angles M and N ?(1 point)m∠M =° and m∠N =°
Since triangle LMN is isosceles, we know that angle L is congruent to angle N. Given that m∠L = 36°, it means that m∠N = 36° as well. Since angles in a triangle add up to 180°, we can calculate the measure of angle M.
m∠M + m∠L + m∠N = 180°
m∠M + 36° + 36° = 180°
m∠M + 72° = 180°
m∠M = 180° - 72° = 108°
Therefore, m∠M = 108° and m∠N = 36°.