If m∠A = 5x −12 m ∠ A = 5 x − 12 , m∠B = 1x+18 m ∠ B = 1 x + 18 , ∠A ∠ A and ∠C ∠ C are supplementary, and ∠B ∠ B and ∠C ∠ C are supplementary, find x.

Answer 1

angle A + angle C = 180 and angle B + angle C = 180

(5x-12) + C = 180 AND (x + 18) + C = 180

(5x-12) + C = (x + 18) + C <-- substitution/transitive

5x-12 = x+18 <-- C cancels out

4x-12 = 18

4x = 30

x = 30/4 = 15/2 = 7.5

angle A = 5x-12 = 5*7.5 - 12 = 25.5

angle B = x+18 = 7.5 + 18 = 25.5

C = 180 - 25.5 = 154.5

Answer 2

Since ∠A and ∠C are supplementary then m∠A + m∠C = 180. So, subtracting m∠C from both sides, we can say that m∠A = 180 - m∠C

Since ∠B and ∠C are supplementary then m∠B + m∠C = 180. So, subtracting m∠C from both sides, we can say that m∠B = 180 - m∠C

Since both m∠A and m∠B equal the same thing (180 - m∠C), then they must be equal to themselves. So:

5x − 12 = 1x + 18 [adding 12 tp both sides we get:

5x = 1x + 30 [subtracting 1x from both sides we get:

4x = 30 [dividing both sides by 4 we get:

x = 30/4 = 7.5 (or 15/2)