Question

The angles of quadrilateral are in the ratio of 2:3:5:8 find the measure of each angle​

Answer 1

Answer:

Given :-

• The angles of a quadrilateral are in the ratio of 2:3:5:8.

To Find :-

• What is the measure of each angles.

Solution :-

» Let, the first angle be 2x

» Second angle be 3x

» Third angle be 5x

» And, the fourth angle will be 8x

We know that,

★ Sum of all angles of a quadrilateral = 360° ★

According to the question by using the formula we get,

⇒ 2x + 3x + 5x + 8x = 360°

⇒ 5x + 13x = 360°

⇒ 18x = 360°

⇒ x = 360°/18

➠ x = 20°

Hence, the required angles are,

✧ First angle = 2x = 2(20°) = 40°

✧ Second angle = 3x = 3(20°) = 60°

✧ Third angle = 5x = 5(20°) = 100°

✧ Fourth angle = 8(20°) = 160°

∴ The measure of each angle of a quadrilateral are 40°, 60°, 100° and 160°.

Let's Verify :-

↦ 2x + 3x + 5x + 8x = 360°

Put x = 20° we get,

↦ 2(20°) + 3(20°) + 5(20°) + 8(20°) = 360°

↦ 40° + 60° + 100° + 160° = 360°

↦ 360° = 360°

➦ LHS = RHS

Hence, Verified ✔

Answer 2

Answer:

Given :-

• Angles of Quardilateral 2:3:5:8

To Find :-

Measure of each angle

Solution :-

As we know that

Sum of all angles in a Quadrilateral is 360⁰. This is also known as angle sum property.

Let, the angles be 2x,3x,5x and 8x

$\tt \implies 2x + 3x + 5x + 8x = 360$

$\tt \implies \: 5x + 13x = 360$

$\tt \implies \: 18x = 360$

$\tt \implies \: x = \dfrac{360}{18}$

$\tt \implies \:x \: = 20$

Angles are

$\sf \: 2x = 2(20) = 40$

$\sf \: 3x = 3(20) = 60$

$\sf \: 5x = 5(20) = 100$

$\sf \: 8x = 8(20) = 160$