Question

If complementary of an angle is equal to 3 times
of supplementary of this angle then find the
measurement of its angle.
​

Answer 1

Supplement is 135°

Step-by-step explanation:

• Let X be an angle, so thrice of it is 3X.

• The complement of X = supplement of 3X.

• two adjacent angles are called complementary if their sum is 90 degree, on the other hand, they will be called supplementary if the sum is 180 degrees.

therefore,

$90-X= 180 - 3X$

$3X - X = 180-90$

$2X=90$

$x=45$

So the angle is 45° Its complement is 45 and the supplement is 135°

Answer 2

ANSWER:-

Given:

If complement of an angle is equal to 3 times of supplementary of this angle.

To find:

The measurement of its angle.

Explanation:

Let the required angle be R

• Complement angle= 90-R

∠A +∠B equal to 90° are called complementary angle.

∠A+∠B= 90°

∠A= 90° - ∠B

• Supplement angle= 180- R

∠A+ ∠B equal to 180° are called supplementary angle.

∠A+∠B= 180°

∠A= 180°- ∠B

According to the question:

Complement angle be R = supplement angle be 3R

⇒ 90°- R= 180°-3R

⇒ -R+3R= (180-90)°

⇒ 2R= 90°

⇒ R= 90°/2

⇒ R= 45°

Thus,

• The complementary angle,R= 45°
• The supplementary angle,3R= [3× 45]°= 135°