Question

∠A and ∠ B ∠B are supplementary angles. If m ∠ A = ( 7 x + 15 ) ∘ ∠A=(7x+15) ∘ and m ∠ B = ( x + 13 ) ∘ ∠B=(x+13) ∘ , then find the measure of ∠ A ∠A.

Answer 1

∠A = 148°

∠B = 32°

Explanation:

We know that ∠A and ∠B are supplementary angles, this means that:

∠A + ∠B = 180°

And we also know that:

∠A = (7x + 15)°

∠B = (x + 13)°

Then we have a system of 3 equations.

To solve it, we can replace the second and third equations into the first one, and get:

(7x + 15)° + (x + 13)° = 180°

Now we can solve this for x, but first, let's remove the degree sign so it is easier to work:

7x + 15 + x + 13 = 180

(7 + 1)*x + 28 = 180

8*x = 180 - 28 = 152

x = 152/8 = 19

Now that we know x, we can find the values of ∠A and ∠B

∠A = (7x + 15)° = (7*19 + 15)° = 148°

∠B = (x + 13)° = (19 + 13)° = 32°