Question

in a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of angle A.​

Answer 1

Given data : In a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C.

To find : The measure of angle A.

Solution :

According to given,

→ ∠A = ∠B - 40

→ ∠B = ∠A + 40 .......( 1 )

→ ∠A = ∠C - 50

→ ∠C = ∠A + 50 ........( 2 )

we know that, the sum of the measures of the angles is always 180° in a triangle.

Hence,

→ ∠A + ∠B + ∠C = 180

{ from eq. ( 1 ) & ( 2 ) }

→ ∠A + ∠A + 40 + ∠A + 50 = 180

→ 3 *∠A + 90 = 180

→ 3 *∠A = 180 - 90

→ 3 *∠A = 90

→∠A = 90/3

→ ∠A = 30°

Hence, the measure of ∠A is 30°.

{ More info :

from eq. ( 1 )

→ ∠B = ∠A + 40

put value of ∠A

→ ∠B = 30 + 40

→ ∠B = 70°

from eq. ( 2 )

→ ∠C = ∠A + 50

put value of ∠A

→ ∠C = 30 + 50

→ ∠C = 80° }