∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left bracket, 7, x, minus, 12, right bracket, degreesm∠1=(7x−12)

Question

∘
and m, angle, 2, equals, left bracket, 7, x, minus, 18, right bracket, degreesm∠2=(7x−18)
∘
, then find the measure of angle, 1∠1

Answer 1

To find the measure of angle 1 ( ∠1 ), we know that angle 1 and angle 2 are supplementary angles, meaning the sum of their measures is 180 degrees.

So, we can set up the equation:

m∠1 + m∠2 = 180

Substitute the given values:

(7x-12) + (7x-18) = 180

Combine like terms:

14x - 30 = 180

Add 30 to both sides:

14x = 210

Divide by 14:

x = 15

Now, substitute x back into m∠1 to find the measure of angle 1:

m∠1 = 7x - 12
m∠1 = 7(15) - 12
m∠1 = 105 - 12
m∠1 = 93

Therefore, the measure of angle 1 ( ∠1 ) is 93 degrees.