∠A and ∠ B ∠B are supplementary angles. If m ∠ A = ( 7 x − 15 ) ∘ ∠A=(7x−15) ∘ and m ∠ B = ( 2 x − 3 ) ∘ ∠B=(2x−3) ∘ , then find the measure of ∠ A ∠A.

Answer 1

Supplementary angles have a sum of 180°

Therefore, we can add the expressions for Angles A and B and set their sum equal to 180.

( 7x - 15 ) + ( 2x - 3 ) = 180

Now we can combine like terms and use inverse operations to find the value of x:

( 7x - 15 ) + ( 2x - 3 ) = 180

9x - 18 = 180

9x - 18 + 18 = 180 + 18

9x = 198

9x/9 = 198/9

x = 22

Then Angle A will have a measure of 7x - 15 or 7• 22 -15 = 154 - 15 = 139°

m∠A = 139°

The measure of Angle b will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°

m∠ B = 41°

NOTE: 139 + 41 = 180