∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left bracket, 4, x, minus, 23, right bracket, degreesm∠1=(4x−23)

Question

∘
and m, angle, 2, equals, left bracket, 2, x, plus, 11, right bracket, degreesm∠2=(2x+11)
∘
, then find the measure of angle, 1∠1.

Answer 1

Since angles 1 and 2 are supplementary, we know that their measures sum up to 180 degrees:

m∠1 + m∠2 = 180

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

(4x - 23) + (2x + 11) = 180
6x - 12 = 180
6x = 192
x = 32

Now, find the measure of angle 1:

m∠1 = (4x - 23)
m∠1 = (4(32) - 23)
m∠1 = (128 - 23)
m∠1 = 105 degrees

Therefore, the measure of angle 1 is 105 degrees.