Question

Find the value of ‘x’ and ‘y’ in the adjacent figure.

Answer 1

In ∆ACL, AC = CL 

So, ∆ACL is an isosceles triangle.

In isosceles triangle, the angles which are opposite to equal sides are also equal. 

So, ∠A = ∠L = x° ∠C = 56° (Vertically opposite angle) 

In ∆ACL, we know ∠A + ∠C + ∠L = 180° 

⇒ x + 56° + x = 180° 

⇒ 2x + 56° – 56° = 180° – 56°

 ⇒ 2x =124° 

⇒ 2x/2 = 124°/2

∴ x = 62° 

Exterior angle at A = ∠C + ∠L 

⇒ y = 56 + 62 

⇒ y = 118°