∠A and \angle B∠B are supplementary angles. If m\angle A=(4x-30)^{\circ}∠A=(4x−30) ∘
and m\angle B=(4x-14)^{\circ}∠B=(4x−14)
∘
, then find the measure of \angle A∠A.

the measure of ∠A. is 87∘

Step-by-step explanation:

Two angles are said to be supplementary angles if the sum of those angles is 180 degrees.

Given

∠A=(4x−30) ∘

∠B=(4x−14) ∘

Fir angles to be supplementary

∠A + ∠B = 180

(4x−30) ∘ + (4x−14) ∘ = 180∘

(8x -54 )∘ = 180∘

=> 8x =  180∘ +  54∘= 234∘

=> x = 234∘/8 = 29.25∘

Thus,

∠A=(4x−30) ∘

∠A=(4*29.25−30) ∘ =( 117 - 30 ) ∘ = 87∘

Thus,

the measure of ∠A. is 87∘