Find the values of x and y in the figures given below.

i.

ii.

iii.

(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