Answer:
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°