Question

∆ ABC, ∠A +∠B = 116° and ∠B + ∠C = 126°. The measure of angles ∠A, ∠B and ∠C are

Answer 1

To find :-

• we need to find measure of angles ∠A, ∠B and ∠C

Solution :

• ∠A +∠B = 116° .....1)
• ∠B + ∠C = 126° ......2)

From equation (1)

⠀⠀⠀⠀⠀⠀∠A +∠B = 116

⠀⠀⠀⠀⠀⠀∠B = 116 - ∠A .....3)

From equation (2)

⠀⠀⠀⠀⠀⠀∠B + ∠C = 126°

⠀⠀⠀⠀⠀⠀116 - ∠A + ∠C = 126°

⠀⠀⠀⠀⠀⠀∠C - ∠A = 126 - 116

⠀⠀⠀⠀⠀⠀∠C = 10 + ∠A ....(4)

We know that,

♻️Sum of all angles of triangle = 180

So,

∠A + ∠B + ∠C = 180

• From (3) and (4)

⟶ ∠A + (116 - ∠A) + 10 + ∠A = 180

⟶ ∠A + 116 - ∠A + 10 + ∠A = 180

⟶ ∠A + 126 = 180

⟶ ∠A = 180 - 126

⟶ ∠A = 54

So,

⇝∠B = 116 - ∠A

⇝∠B = 116 - 54

⇝∠B = 62

And

›› ∠C = 10 + ∠A

›› ∠C = 10 + 54

›› ∠C = 64

Hence,

Measure of all angles of ∆ABC are :-

• ∠A = 54
• ∠B = 62
• ∠C = 64

Verification :-

Sum of all angles of triangle = 180

››➔ ∠A + ∠B + ∠C = 180

››➔ 54 + 62 + 64 = 180

››➔ 54 + 126 = 180

››➔ 180 = 180

LHS = RHS

Hence VERIFIED.

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