Question

3. The angles of pentagon are in the ratio 1 ∶ 2 ∶ 4 ∶ 1 ∶ 2. If the sum is 540. Find measure of

each angle.​

Answer 1

Step-by-step explanation:

let the angles be x,2x,4x,x,2x

As , x+2x+4x+x+2x=540

10x=540

x=540/10

x=54

first angle measures =54

second angle measures =2×54

=108

third angle measures=216

fourth angle measures=54

fifth angle measures=108

check=54+108+216+54+108=540

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Answer 2

Given :-

Ratio of angles of a pentagon = 1 ∶ 2 ∶ 4 ∶ 1 ∶ 2

Sum of the angles of a pentagon = 540

To Find :-

The measure of each angle.

Analysis :-

Consider the common ratio as a variable.

Multiply the variable to each angle given.

Make an equation accordingly.

Then find the value of the variable.

Substitute the value of the variable and substitute the value in each angle.

Solution :-

Consider the common ratio as 'x' angle.

Ratio of angles of a pentagon = 1 ∶ 2 ∶ 4 ∶ 1 ∶ 2

Then the five angles would be x, 2x, 4x, x, 2x respectively.

Given that,

Sum of the angles of a pentagon = 540

Making an equation,

x + 2x + 4x + x + 2x = 540°

10x = 540°

x = 540/10

x = 54°

Therefore, the value of x is 54°.

Substituting the value of x,

x = 54°

2x = 2 × 54 = 108°

4x = 4 × 54 = 216°

x = 54°

2x = 2 × 54 = 108°

Therefore, the angles of a pentagon are 54°, 108°, 216°, 54° and 108°.