Question

if a pair of complementary angles are the ratio 3 :6 then find the biger angle​

Answer 1

Answer:

The greater angle is 60°.

Step-by-step-explanation:

The complementary angles are in ratio 3 : 6.

Let the common multiple be x.

Greater angle = 6x

Smaller angle = 3x

We know that,

The sum of two complementary angles is 90°.

⇒ Greater angle + Smaller angle = 90°

⇒ 6x + 3x = 90

⇒ 9x = 90

⇒ x = 90 ÷ 9

⇒ x = 10

Now,

Greater angle = 6x

⇒ Greater angle = 6 * 10

⇒ Greater angle = 60°

∴ The greater angle is 60°.

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Additional Information:

1. Complementary angles sum upto 90°.

2. In a right angled triangle, the two angles besides right angle are complementary.

3. Supplementary angles sum upto 180°.

4. Two right angles, each of 90°, are supplementary angles.

Answer 2

Step-by-step explanation:

$\huge{\purple{\sf{ \underline{ \underline{Explanation : }}}}}$

$\sf{Let \: the \: angle \: be \: 3x \: and \: 6x}$

We know,

$\boxed{ \sf{Complementary \: angle \: = 90 \degree}}$

So According to question :

$\large{ \sf{(3x + 6x) = 90 \degree}}$

$\large{ \sf{⟹ \: 9x = 90 \degree}}$

$\large{ \sf{⟹ \: x = \frac{90}{9} }}$

$\large{ \sf{⟹ \: x \: = 10}}$

$\sf{We \: got } \\ \: \bold{x = 10}$

Given Ratios :

• 3
• 6

So , multiply 3 and 6 by 10

$\large{ \sf{⇒ \: 10 \: \times \: 3}}$

$\large{ \sf{⇒ \: 30}}$

$\large{ \sf{⇒ \: 10 \times 6}}$

$\large{ \sf{⇒ \: 60 \degree}}$

We got :

60° and 30°

The bigger angle is 60°