Answer:
1) ∠Q = 110
2) ∠a + ∠b + ∠c + ∠d = 360
Explanation:
1) By kite property, the sum of angles is 360 and ∠Q = ∠O
⇒ ∠N + ∠P + ∠Q + ∠O = 360
⇒ 85 + 55 + 2∠Q = 360
⇒ 140 + 2∠Q = 360
⇒ 2∠Q = 360-140
⇒ 2∠Q = 220
⇒ ∠Q = 110
2)By property, the sum of exterior angles is 360
Proof:
∠a + 120 = 180 (straight line)
⇒ ∠a = 60
∠b + 70 = 180
⇒ ∠b = 110
∠c + 80 = 180
⇒ ∠c = 100
∠d + 90 = 180
⇒ ∠d = 90
⇒ ∠a + ∠b + ∠c + ∠d = 60 + 110 + 100 + 90 = 360