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Question 842478: 1. The exterior sides of two adjacent angles make a right angle. The first angle has a measure that is 6 more than half of the second. What are the measures of both angles?
2. Two angles are supplementary. The measure of one angle is 5 greater than 40% of the other. Find the measures of both angles.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the exterior sides of 2 adjacent angles is a right angle, then the sum of the 2 interior angles is equal to 90 degrees.
if you let x equal the measure of the smaller angle, then x+6 equal the measure of the bigger angle.
since the sum of the angles is equal to 90 degrees, you get:
x + x + 6 = 90 which simplifies to:
2x + 6 = 90
subtract 6 from both sides of this equation to get:
2x = 84
divide both sides of this equation by 2 to get:
x = 42
the smaller angle is 42.
the bigger aqngle is 48.
the sum of the angles is 90 degrees which is a right angle.
if the angles are supplementary, then their sum is 180 degrees.
if you let x equal the measure of one of the angles, then the other angle is equal to .40x + 5
since the sum of the angles is equal to 180, you get:
x + .40x + 5 = 180
subtract 5 from both sides of this equation to get:
x + .40x = 175
combine like terms to get:
1.40x = 175
divide both sides of this equation by 1.40 to get:
x = 175/1.4 = 125
one of the angles measures 125 degrees.
the other angle measure .40 * 125 + 5 which is equal to 55 degrees.
the sum of the angles is equal to 125 + 55 = 180.
your solution is:
one angle measures 125.
the other angles measures 55.
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