Question

please answer this question​

Answer 1

Given:-

In Δ ABC,

Side AB and BC are Produced    and,

AB = BC.

Solution:-

In Δ ABC,

∠A = ∠C          --- (i)     [ Angle opposite to equal sides are equal ]

now, ∠A + ∠B + ∠C = 180°             [ Angle Sum Property ]

∠A + 54° + ∠A = 180°             [ from equation (i) ]

2∠A = 180° - 54°

∠A = $\dfrac{126}{2}$

∠A = 63°

∠A = ∠C = 63°

so, ∠A + ∠B = a                [ Exterior angle property of triangles ]

63° + 54° = a

a = 117°

and, ∠B + ∠C = b               [ Exterior angle property of triangles ]

54° + 63° = b

b = 117°

so, a = b = 117°

Some Important Terms:-

• Sum of all angles of Triangle is 180°.

• Sum of two opposite interior angle is equal to one exterior angle.

• Angle opposite to equal sides are equal  OR  Side opposite to equal angles are equal.

• Sum of all Exterior angles of triangle is 360°.