In the figure, MNP and PQR are isosceles triangles where MP = NP and PQ = PR. Given that QS, RU and MW are straight lines, find
- ∠TXW
- ∠RSX
(a)
∠MNP = ∠NMP = ∠PQR = ∠PRQ (Isosceles triangle)
∠PRQ = ∠SRX = 46° (Verticallly opposite angles)
∠URX
= 46° - 12°
= 34°
∠RTX
= 180° - 105°
= 75° (Angles on a straight line)
∠TXW
= 75° + 34°
= 109° (Exterior angle of a triangle)
(b)
∠RSX
= 109° - 46°
= 63° (Exterior angle of a triangle)
Answer(s): (a) 109°; (b) 63°