Question

The ratio of two complementary angles is 4 : 5. Find these angles and ratio of their supplementary angles.

I need step by step answers ​

Answer 1

Step-by-step explanation:

4:5

let one angle =4x

other angle =5x

A.T.Q.

Sum of complementary angles =90

4x+5x=90

9x=90

x=90/9

x=10

So,

one angle= 4x

=4(10)

= 40

Other angle = 5x

= 5(10)

=50

Answer 2

Question :

The ratio of two complementary angles is 4 : 5. Find these angles and ratio of their supplementary angles.

Let us assume :

The angles be x

So,

First angle is 4 = 4x

Second angle is 5 = 5x

Solution :

We know that sum of two complementary angles is 90°

So by applying this we get :

• 4x + 5x = 90°

• 9x = 90°

Transposing 9 to the left hand side of the equation we get :

• x = 90°/9

• x = 10°

Now, we need to get the exact values instead of x

1) 4x

⟹ 4 × 10°

⟹ 40°

Therefore, the first angle is 40°

2) 5x

⟹ 5 × 10°

⟹ 50°

Hence, the second angle is 50°

We got the first part of this sum and now to get the second part i.e. to find the ratio of Supplementary angles

We know that

3∠s of a ∆ = 180°

So,

• The first supplementary angle = 180° - 40° ⟹ 140°

• The second supplementary angle = 180° - 50° ⟹ 130°

Hence,

Their ratio is 140 : 130

140 can be written as 14 × 10

130 can be written as 13 × 10

So, we get

⟹ 14 × 10 = 13 × 10

Transposing 10 we get

⟹ 14 = 13 × 10/10

10 will be cancelled

⟹ 14 = 13

Hence the ratio of standard angle is 14 : 13