Question

In ∆ABC, angle A + angle B = 116°, angle B + angle C = 126°. Find the measure of each angle of the triangle.

Answer 1

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Answer 2

$\large\underline\pink{Given:-}$

• In ∆ABC, angle A + angle B = 116°, angle B + angle C = 126°.

$\large\underline\pink{To find:-}$

• Find the measure of each angle of the triangle. ....?

$\large\underline\pink{Solutions:-}$

In ∆ABC

• <A + <B = 116° ___________(i).
• <B + <C = 126° __________(ii).

from equation (i).

<A + <B = 116°

<B = 116 - <A ___________(iii).

from equation (ii).

<B + <C = 126°

<C - <A = 126 - 116

<C = 10 + <A ____________(iv).

Sum of all angle of triangle = 180

<A + <B + <C = 180°

<A + (116 - <A) + 10 + <A = 180

<A + 126 = 180

<A = 54°

Now,

<B = 116 - <A

<B = 116 - 54

<B = 62°

<C = 10 + <A

<C = 10 + 54

<C = 64°

hence, the measures of all angle of ∆ABC are :-

• <A = 56° , <B = 62°, <C = 64°