Question

Question 3 Please. I'm really stuck :(

Answer 1

Answer B - 70 degrees
Triangle STU is an isosceles one. Angle s is 40. Find angle TSR (180-40)/2 = 70. Now find angle SRT (180-70)/2 = 55. Being isosceles angle SRT = angle USQ = 55. Now find angle TPU (180-(55+55)) = 70

Answer 2

let ∠RTS=∠RST = a (say)
∠QUA=∠QSU= b(say)
then we know , at point S, a+40+b=180. so, a+b=140 we'll use this later.

consider trianglePQR, ∠P+∠Q+∠R=180
i.e.P+(180-2b)+(180-2a)=180
P+180+180-2(a+b)=180 ⇒P+180-2(a+b)=0 ⇒P=2(140)- 180=280-180=100
hence,answer is E