Short Answer C Nice little problem. The catch is that alpha and beta both add up to 90 degrees. Here's why.
α + β + right angle = 180° All triangles have 180° A right and = 90°. α + β + 90 = 180 Right angles are 90° Now subtract 90° from both sides α + β = 180 - 90 α + β = 90
Now all you have to do is put in the x values for alpha and beta and equate them to 90
5x/3 + 20 + 2x/3 + 14 = 90 Collect the light terms. 5x/3 + 2x/3 + 20 + 14 = 90 7x/3 + 34 = 90 Subtract 24 from both sides. 7x/3 = 90 - 34 7x/3 = 56 Multiply by sides by 3 7x = 3*56 7x = 168 Divide by 7 x = 168/7 x = 24
