Question

the sum of an amgle and one third of its supplementry angle is 90°. the measure of the angle is
a) 135°
b)120°
c) 60°
d)45°​

Answer 1

$\green\bigstar$ Answer:

The angle is 45°.

• Hence, the correct option is (d) 45°

$\blue\bigstar$Given:

• The sum of an angle and one third of its supplementary angle is 90°.

$\red\bigstar$To find:

• The measure of that angle.

$\pink\bigstar$ Solution:

Let the unknown angle be x.

It's supplementary angle = 180° - x

A/q

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

$\implies \: x \: + \: \frac{180 \degree}{3} - \frac{x}{3} = 90 \degree$

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

$\implies \: x \: - \: \frac{x}{3} = 90 \degree - \: 60 \degree$

$\implies \: \frac{3x}{3} - \frac{x}{3} = 30 \degree$

$\implies \: \frac{(3x \: - \: x)}{3} = 30 \degree$

$\implies \: 3x - \: x \: = 3 \times (30 \degree)$

$\implies \: 2x \: = 90 \degree$

$\implies \: x \: = \: \frac{90 \degree}{2}$

$\implies \: x \: = \: 45 \degree$

$\therefore$ the angle is 45°.

$\blue\bigstar$Extra - Information:

$\rightarrow$ Two Angles are Supplementary when they add up to 180°.

$\rightarrow$ When the sum of the adjacent angles is 180°, then the angles are supplementary. And they will also form a linear pair.

$\rightarrow$ It is not necessary that supplementary angles are always adjacent and hence, not all supplementary angles will form a linear pair.

$\rightarrow$ All linear pair of angles are supplementary, but not all supplementary angles will form a linear pair.

Answer 2

Answer:

45° is the right answer.........