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.
1 answer:
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
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