Question

Isosceles and equilateral triangles (please help me as fast as you can thank you)

Answer 1

x = 71°

x = 19°

x = 34°

Explanation:

In rectangle ABCD. By exterior angle theorem:

x + 65° = 46° + 90°

x + 65° = 136°

x = 136° - 65°

x = 71°

Since, XYZ is an equilateral triangle,

Therefore, m(angle XZY) = 60°, So, by exterior angle theorem:

m angle XZY = x + 41°

60° = x + 41°

60° - 41° = x

19° = x

x = 19°

PQR is an isosceles triangle. In which PQ = PR.

Therefore,

m(angle PRQ) = m(angle PQR) = 69°

By exterior angle theorem:

x + 35° = 69°

x = 69° - 35°

x = 34°