SOLUTION: 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. 2. The measures of two angles

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.
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?
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.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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.
:
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
:
:
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?
=
:
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.
:
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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:
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