Question 88478
1.The sum of the complement and supplement of an acute angle exceeds 20 less than thrice its compliment by 60. Find the measure of the acute angle.
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Acute angle = x
(90-x) + (180-x) - 60 = 3(90-x)- 20
270 - 2x - 60 = 270 - 3x - 20
210 - 2x = 250 - 3x
+3x - 2x = 250 - 210
x = 40 degrees
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2. The measures of two angles are in the ratio of 4:5. The larger of the angles is 60 less than twice the smaller angle. Find the measure of each angle. Are they complementary or supplementary?
{{{4/5}}} = {{{x/((2x-60))}}}
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Cross multiply:
4(2x-60) = 5x
8x - 240 = 5x
8x - 5x = +240
3x = 240
x = 240/3
x = 80 degrees
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Find the larger angle:
2(80) - 60 = 100 degrees
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The two angles are supplementary
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3. What is the measure of an angle if twice the measure of its supplement is 30 more than 5 times the measure of its complement.
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2(180-x) = 5(90-x) + 30
360 - 2x = 450 - 5x + 30
360 - 2x = 480 - 5x
+5x - 2x = 480 - 360
3x = 120
x = 120/3
x = 40 degrees
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