anonymous
  • anonymous
The sum of the measures of two complementary angles exceeds the difference of their measures by 72°. Find the measure of the smaller angle. 18° 36° 54° 58°
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
Angle: x Complement: 90 - x
mathstudent55
  • mathstudent55
Sum of the complements: x + 90 - x = 90
anonymous
  • anonymous
2x??

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More answers

mathstudent55
  • mathstudent55
Difference of their measures: x - (90 - x)
mathstudent55
  • mathstudent55
90 exceeds x - (90 - x) by 72 That means: 90 - [x - (90 - x)] = 72
mathstudent55
  • mathstudent55
Solve for x.
anonymous
  • anonymous
....
anonymous
  • anonymous
i distribute the negitive?
mathstudent55
  • mathstudent55
If x is more than 45, then subtract x from 90
anonymous
  • anonymous
so it would be a
anonymous
  • anonymous
A
mathstudent55
  • mathstudent55
90 - [x - (90 - x)] = 72 90 - [x - 90 + x] = 72 90 - [2x - 90] = 72 90 - 2x + 90 = 72 -2x + 180 = 72 -2x = -108 x = 54 The measure of one of the angles is 54. Since complementary angles add to 90, the other angle is 90 - x. 90 - 54 = 36 Since they ask fot eh measure of the smaller angle, the answer is 36.
anonymous
  • anonymous
thank you man that much simpler
mathstudent55
  • mathstudent55
^the last sentence above should read: Since they ask for the measure of the smaller angle, the answer is 36.
mathstudent55
  • mathstudent55
You're welcome.

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