Question

Find mABC.
A. 102°
B. 54°
C. 14°
D. 78°

Answer 1

D = 78

Explanation:

The two angles form a straight line so they add to 180

4x+22 + 8x-10 = 180

Combine like terms

12x +12 =180

Subtract 12 from each side

12x+12-12 = 180-12

12x = 168

Divide by 12

12x/12 =168/12

x=14

We want to find ABC

4x+22 = 4*14+22 = 56+22 = 78

Answer 2

By the supplementary angles theorem, we know that both of the angles add up to equal 180°, so:

(4x + 22) + (8x - 10) = 180

12x + 12 = 180

12x = 168

x = 14

Now you just have to plug in x into the value for ∠ABC:

∠ABC = 4x + 22

∠ABC = 4(14) + 22

∠ABC = 46 + 22

∠ABC = 68°