Question

Two supplementary angles are in the ratio 9:3. Find the measure of the angles.

Answer 1

Answer:

Given :-

• Two supplementary angles are in the ratio of 9 : 3.

To Find :-

• What is the measure of the angles.

Solution :-

Let,

$\mapsto \bf First\: Angle =\: 9x$

$\mapsto \bf Second\: Angle =\: 3x$

As we know that :

$\footnotesize\bigstar\: \: \sf\boxed{\bold{\pink{Sum\: of\: two\: supplementary\: angles =\: 180^{\circ}}}}$

According to the question by using the formula we get,

$\implies \sf 9x + 3x =\: 180^{\circ}$

$\implies \sf 12x =\: 180^{\circ}$

$\implies \sf x =\: \dfrac{\cancel{180^{\circ}}}{\cancel{12}}$

$\implies \sf x =\: \dfrac{15^{\circ}}{1}$

$\implies \sf\bold{\purple{x =\: 15^{\circ}}}$

Hence, the required measures of the angles are :

❒ First Angle :

$\longrightarrow \sf First\: Angle =\: 9x$

$\longrightarrow \sf First\: Angle =\: 9 \times 15^{\circ}$

$\longrightarrow \sf\bold{\red{First\: Angle =\: 135^{\circ}}}$

❒ Second Angle :

$\longrightarrow \sf Second\: Angle =\: 3x$

$\longrightarrow \sf Second\: Angle =\: 3 \times 15^{\circ}$

$\longrightarrow \sf\bold{\red{Second\: Angle =\: 45^{\circ}}}$

${\small{\bold{\underline{\therefore\: The\: measures\: of\: two\: supplementary\: angles\: are\: 135^{\circ}\: and\: 45^{\circ}\: respectively\: .}}}}$

Answer 2

Step-by-step explanation:

Let angles be 9 x and 3 x respectively.

ACQ

9 x +3 x=180

x=15

Ans - 135°,45°