Answer
𝑚 = 20 degrees
𝑛 = 45 degrees
Work Step by Step
2 sides of the INNER isosceles triangle are equal - given
If both sides are equal, then both base angles are equal - Theorem 4-3 Isosceles Triangle Theorem
Vertex of INNER isosceles triangle = 90 degrees - given
90 + 𝑛 + 𝑛 = 180
2𝑛 = 90
𝑛 = 45 degrees
2 sides of the OUTER isosceles triangle are equal - given
If both side are equal, then both base angles are equal - Theorem 4-3 Isosceles Triangle Theorem
Base angle = (𝑚 + 𝑛) - given
𝑛 = 45 - worked out above
50 + (𝑚 + 𝑛) + (𝑚 + 𝑛) = 180
50 + (𝑚 + 45) + (𝑚 + 45) = 180
(𝑚 + 45) + (𝑚 + 45) = 180 - 50
2(𝑚 + 45) = 130
(𝑚 + 45) = 65
𝑚 = 20 degrees
