∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left bracket, 7, x, minus, 11, right bracket, degreesm∠1=(7x−11)

Question

∘
and m, angle, 2, equals, left bracket, x, minus, 25, right bracket, degreesm∠2=(x−25)
∘
, then find the measure of angle, 2∠2.

Answer 1

Since supplementary angles add up to 180 degrees, we can set up the equation:

m∠1 + m∠2 = 180

Substitute the given values:

(7x - 11) + (x - 25) = 180

Combine like terms:

8x - 36 = 180

Add 36 to both sides:

8x = 216

Divide by 8:

x = 27

Now substitute x back into m∠2 to find the measure of angle 2∠2:

m∠2 = x - 25
m∠2 = 27 - 25
m∠2 = 2 degrees

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