SOLUTION: In a right triangle, the smallest angle is 16 smaller than the next smallest angle. Find the measures of the angles.

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Question 663202: In a right triangle, the smallest angle is 16 smaller than the next smallest angle. Find the measures of the angles.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

In a right triangle one angle is 90 degrees, and the sum of all is 180 degrees,
let alpha be the smallest angle
if alpha is 16 smaller than the next smallest angle beta, then
alpha%2B16=beta
so, we will have
alpha%2Bbeta%2B90=180

alpha%2Bbeta=90 ....replace beta=alpha%2B16
alpha%2Balpha%2B16=90...solve for alpha
2alpha=90-16
2alpha=74
alpha=74%2F2
highlight%28alpha=37%29

now find beta
beta=alpha%2B16
beta=37%2B16
highlight%28beta=53%29