Question

The measure of a given angle is1/4times that of its supplimentry angle find the measure of complementary angle​

Answer 1

Answer:

If the measure of a given angle is 1/4 times that of its supplementary angle, then the measure of its complementary angle is 54°

Step-by-step explanation:

Given that the measure of a given angle is 1/4 times that of its supplementary angle.

Let X be the given angle and Y be its supplementary angle.

Given X = $\frac{1}{4} *Y$

As X and Y are supplementary angles, X + Y = 180

Substitute X= $\frac{1}{4} *Y$

That is X + Y = 180

$\frac{1}{4} *Y$ + Y = 180°

$\frac{Y+4Y}{4} =180\\\\ 5Y= 180*4\\\\ Y=\frac{180*4}{5} \\\\ Y=36*4\\\\ Y= 144$

Therefore, the supplementary angle Y is 144°

X = $\frac{1}{4} *Y$

= $\frac{1}{4} *144$

=36°

Therefore, the given angle is 36°

Let Z be the complementary angle of X

As X and Z are complementary angles, X + Z=90°

That is, 36+Z= 90

Z= 90-36 = 54°

So the complementary angle of the given angle is 54°