∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left bracket, 2, x, minus, 21, right bracket, degreesm∠1=(2x−21)

Question

∘
and m, angle, 2, equals, left bracket, 4, x, plus, 15, right bracket, degreesm∠2=(4x+15)
∘
, then find the measure of angle, 2∠2.

Answer 1

Since ∠1 and ∠2 are supplementary angles, we have:

m∠1 + m∠2 = 180

Substitute the given expressions for m∠1 and m∠2:

(2x - 21) + (4x + 15) = 180

Combine like terms:

6x - 6 = 180

Add 6 to both sides:

6x = 186

Divide by 6:

x = 31

Now substitute x back into the expression for m∠2:

m∠2 = 4(31) + 15
m∠2 = 124 + 15
m∠2 = 139 degrees

Therefore, the measure of angle 2∠2 is 139 degrees.