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.

α = 56° is the answer.

Step-by-step 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°

what is the original number? you forgot to add it.