Question

∠A and \angle B∠B are supplementary angles. If m\angle A=(7x+10)^{\circ}∠A=(7x+10) ∘ and m\angle B=(7x-26)^{\circ}∠B=(7x−26) ∘ , then find the measure of \angle A∠A.

Answer 1

108 degrees

Explanation:

Since angles A and B are supplementary, they both add up to 180. Angle A = 7x+10, and angle B = 7x-26. You can set up the equation A + B = 180, and then plug in angles A and B, which gives you 7x+10 + 7x-26 = 180. Then you just need to isolate x:

Combine like terms: 14x - 16 = 180

Add 16 to both sides: 14x = 196

Divide both sides by 14: x = 14

Now that you know x, you can plug it into the expression for angle A (7x+10):

A = 7(14) + 10 = 98+10 = 108