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

1.	Find the value of ‘x’ and ‘y’ in the adjacent figure.
Answer» 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°

Answer»

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°

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