9514 1404 393
Answer:
10°, 80°
Step-by-step explanation:
<em><u>Setup</u></em>
Let x and y represent the measures of the two acute angles in the right triangle.
From your knowledge of right triangles, you know the two acute angles are complementary:
x + y = 90
The problem statement gives you another relation:
x = 2(y + 30) . . . . twice the sum ...
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<em><u>Solution</u></em>
The second equation gives you an expression for x that can be substituted into the first equation.
(2(y +30)) + y = 90
3y +60 = 90 . . . . . . . . collect terms
3y = 30 . . . . . . . . . subtract 60
y = 10 . . . . . . . . divide by 3
x = 2(y +30) = 2(40) = 80
The two angles are 10° and 80°.
