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

Solution:-

Sum of all angles in Pentagon = 540° (given)

Let, the ratio of angles be x + 2x +4x +x+2x

Now , We know that the sum of all angles in Pentagon is 540°.

→ x + 2x +4x +x+2x = 540°

→ 10x = 540°

→ x = 540°/10

→ x = 54°

Now , Put the value of x in the given ratio we get

→ x = 54°

→ 2x = 2×54 = 108°

→ 4x = 4×54 = 216°

→ x = 54°

→ 2x = 2×54 = 108°

Therefore , the required angle be 108° , 216° and 54° .

Answer 2

Answer :-

• Angles are 54°, 108°, 216°, 54° and 108°.

Given :-

• The angles of pentagon are in the ratio 1 ∶ 2 ∶ 4 ∶ 1 ∶ 2 and the sum is 540.

To Find :-

• Measure of each angle.

Solution :-

Put x in the ratio

Then

angles are,

• x
• 2x
• 4x
• x
• 2x

As we know that

Sum of all angles of a pentagon is 540°

According to question :-

x + 2x + 4x + x + 2x = 540°

→ 10x = 540°

→ x = 540°/10

→ x = 54°

Put the value of x in the ratio

Now

Angles are,

• x = 54°
• 2x = 2 × 54 = 108°
• 4x = 4 × 54 = 216°
• x = 54°
• 2x = 2 × 54 = 108°

Hence, the angles are 54°, 108°,216°, 54° and 108°.