SOLUTION: 1.) An angle's measure is 18 more than 3 times its complement. Find the measure of the angle. 2.) The supplement of an angle is 4 times as large as the angle's complement. Find

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Question 814229: 1.) An angle's measure is 18 more than 3 times its complement. Find the measure of the angle.
2.) The supplement of an angle is 4 times as large as the angle's complement. Find the measure of the angle.
Thank you for helping.
Found 2 solutions by ewatrrr, thejackal:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

1)An angle's measure is 18° more than 3 times its complement.

Let x represent the angle and (90° - x) represent its complement

Question states******

 x = 3(90°-x) + 18°

Solving for x

 4x = 288°

  x = 72°, the angle, its complement is 18°

CHECKING our Answer*****

  72+=+3%2A18+%2B+18

2)The supplement of an angle is 4 times as large as the angle's complement.

Let x represent the angle, (90° - x)its complement & (180°-x) its supplement

Question states***

 (18°0-x) = 4(90°-x)

Solving for x

  3x = 180°

   x = 60° the angle, complement is 30° and supplement is 120°

CHECKING our Answer***

 120+=+4%2A30

Answer by thejackal(72) About Me  (Show Source):
You can put this solution on YOUR website!
1.) We say that 2 angles compliment each other if the sum of the two angles is equal to 90. Therefore, let angle A be the 1st compliment and angle B be
the angle given as 18 + (3 x A) the sum of 18 + (3 x A) + A = 90; You now have a simple equation. solve for A to find the 1st compliment and then use that value to find the value of angle B
2.) We say that 2 angles supplement each other if the sum of the two angles is equal to 180. Use the same procedure: Angle A is (4 x B) B being A's compliment, therefore 4B + B = 90 , thus 5B = 90 hence B = 18 therefore A the supplement is 90 - 18 = 72; The supplement of A is 180 - 72 = 108
QED