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Two angles are complementary. The larger angle is 15° more than twice the smaller. Find out the measure of the smaller angle.
Let x = the number of degrees in the smaller angle and now let y = the number of degrees in the larger angle. Because the angles are complementary, x + y = 90. Further, since the larger angle is 15 more than twice the smaller, y = 2x + 15. Substitute the second equation inside the ?rst equation for y: x + 2x + 15 = 90. Combine such as terms on the left side of the equation: 3x + 15 = 90. Subtract 15 from both sides of the equation: 3x + 15 - 15 = 90 - 15; simplify: 3x = 75. Divide both sides by 3: 3x/3= 75/3. The variable, x, is now alone: x = 25. The number of degrees in the smaller angle is 25.
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