Question

Angles α and β are the two acute angles in a right triangle, where α = 5x 3 + 20 and β = 2x 3 + 14. Find α.

Answer 1

α = 56° is the answer.

Explanation:

In a triangle sum of all angles = 180°

Since it's a right angle triangle therefore

α + β + 90° = 180°

α + β = 180 - 90 = 90°

Now we put the values of α and β given in the question.

α = 5x³ + 20 , β = 2x³ + 14

Equation becomes

5x³ + 20 + 2x³ + 14 = 90

7x³ + 34 = 90

7x³ = 90 - 34 = 56

x³ = 56/7 = 8

x³ = 2³

therefore x = 2

Now we put the value of x in angle α

α = 5x³ + 14 = 5×2³ + 14

α = 5×8 + 14 = 40 + 14 = 56

α = 56°

Answer 2

The acute angles of a right triangle are complementary, so
α + β = 90
(5x/3 +20) + (2x/3) + 14) = 90 . . . . . . substitute given values
7x/3 +34 = 90 . . . . . . . . . . . . . . . . . . . collect terms
7x/3 = 56 . . . . . . . . . . . . . . . . . . . . . . . subtract 34
x = (3/7)*56 = 24 . . . . . . . . . . . . . . . . . multiply by 3/7

Then the value of α is ...
α = 5*24/3 +20 = 60