Question

The sum of an angle and one third of its supplementary angle is 90 what is the measure of the angle

Answer 1

Let the angle be a

Suplementry angle = 180 - a

According to question

=> a+ (180-a)/3 = 90

=> (3a+180-a)/ 3 = 90

=> 2a+180 = 270

=> 2a = 90

=> a = 45°

Required angle = 45°

Answer 2

Answer:

45°

Step-by-step explanation:

Let the angle be x

Supplementary angles : A Pair of angles whose sum is 180° is called supplementary angles.

Supplement of x = 180°-x

Now we are given that The sum of an angle and one third of its supplementary angle is 90

$x+\frac{1}{3}(180-x)=90$

$x+60-\frac{x}{3}=90$

$x-\frac{x}{3}=90-60$

$\frac{3x-x}{3}=30$

$\frac{2x}{3}=30$

$x=\frac{30 \times 3 }{2}$

$x=45$

Hence the measure of the angle is 45°