Question

Find the measures of the angle, its complement, and its suplement if three times the measure of a suplement of an angle is eight times the measure of a complement of the angle.

Answer 1

The angle, its complement, and its supplement are 36, 54 and 144 degrees respectively

Supplementary and complementary angles

The sum of complementary angles s 90 degrees while that of supplementary angles is 180 degrees.

Let the complement of an angle be 90 -x and its supplement be 180 -x

If three times the measure of a supplement of an angle is eight times the measure of a complement of the angle, then;

3(180-x) = 8(90-x)

Expand

540-3x = 730 - 8x

540-720 = -8x + 3x

180 = 5x

x = 180/5

x = 36 degrees

Complement  = 90 - 36 = 54degrees

Supplement = 180 - 36 = 144 degrees

Hence the angle, its complement, and its supplement are 36, 54 and 144 degrees respectively

Learn more on complement and supplement here; brainly.com/question/13517672

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