Question

Two angles are supplementary.If one of them is one-third of the other. Find the angles

Answer 1

let x be the common multiple.
$x + \frac{1}{3} \times x = 180 \\ x + \frac{x}{3} = 180 \\ \\ 3x + x = 540 \\ x = \frac{540}{4} \\ x = 135$
first angle - 135°
second angle - 45°
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Answer 2

Answer- Q. What are supplementary angles?
==> Two or more angles whose sum is 180° are called supplementary angles or angles on a straight line.
In the question, we are given with two supplementary angles.
Let one angle= x
Second angle= 180°-x
But it is given that, second angle is x/3
So, 180°-x °= x/3
Transposing 3
3(180°-x)= x
540°- 3x= x
540°= 4x
x=540°÷4
x=135°
x/3= 135°÷3= 45°
So, the two supplementary angles are 135° and 45°.
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