Question

Find x in the following figure fast and if you know answer

Answer 1

hope it will help you... ✌

Answer 2

Hi....

Let name the figures as ∆ABC such that in every figure AB = AC.

In first figure,
angle ACB + 120° = 180° [Linear Pairs]
angle ACB = 180°-120° = 60°
angle ABC = angle ACB [Base angles of isosceles triangles are equal]
angle ABC = x = 60°

In second figure,
angle BAC + 110° = 180° [Linear Pairs]
angle BAC = 180°-110° = 70°
angle ACB = angle ABC = x [Base angles of isosceles triangle are equal]
angle BAC + angle ABC + angle ACB = 180° [Sum of all angles of a triangle is always 180°]
70° + x + x = 180°
2x = 180° - 70°
2x = 110°
x = 110°/2 = 55°

In third figure,
angle ABC = 30° [Vertically opposite angles]
angle ABC = angle ACB [Base angles of isosceles triangles are equal]
angle ACB = x = 30°
x = 30°

Hope it helps!