Question

Find the measure of each acute angle in a right triangle where the measure of one acute angle is 3 times the sum of the measure of the other acute angle and 8.

Answer 1

Answer:

α = 20.5

β = 69.5

c = 90

Step-by-step explanation:

we have to make 2 equations one for the relationship between the angles and another for the sum of all the angles

β and α are the acute angles

β = 3α + 8

α + β + 90 = 180

we replace in the second equation the value of β by (3α + 8)

α + β + 90 = 180

α + (3α + 8) + 90 = 180

a + 3a = 180 - 90 - 8

4a = 82

a = 82/4

a = 20.5

now we replace the value of b in the other equation

β = 3α + 8

β = 3 * 20.5 + 8

β =  69.5