Answer :
(i) We know “Sum of all angles of a triangle is 180”.
x + y + 30
= 180
Since it is an isosceles triangle, x = y.
x + x + 30
= 180
⇒ 2x + 30 = 180
⇒ 2x = 180-30
⇒ 2x = 150
⇒ x =
⇒ x = 75
x = y = 75
(ii) We know that “Angles on the opposite sides in the cyclic quadrilateral are supplementary”.
x + 110
= 180
⇒ x = 180-110
⇒ x = 70
y + 85
= 180
⇒ y = 180-85
⇒ y = 95
(iii) Given, x = 90°
x + y + 50
= 180
⇒ 90 + y + 50
= 180
⇒ y + 140 = 180
⇒ y = 180-140
⇒ y = 40
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