Question

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

Answer 1

Answer:

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Answer 2

The measure of all the angles of a quadrilateral are :

• The first angle = 40°.
• The second angle = 60°.
• The third angle = 100°.
• The fourth angle = 160°.

Given :

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

To Find :

• The measure of each angles of a quadrilateral.

Solution :

Let,

The first angle be 2x.

The second angle be 3x.

The third angle be 5x.

The fourth angle be 8x.

We know that,

Sum of all the angles of a quadrilateral are 360°.

I.e.,

$\implies \angle1 + \angle2 + \angle3 + \angle4 = 360 \degree$

First, we need to find the value of x.

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

$\implies 5x + 13x = 360 \degree$

$\implies 18x = 360 \degree$

$\implies x = \cancel\dfrac{360 \degree}{18}$

$\implies x = \cancel\dfrac{180 \degree}{9}$

$\implies x = \cancel\dfrac{60 \degree}{3}$

$\implies x = 20 \degree$

Now, we have to find the angles of a quadrilateral.

So, the angles of a quadrilateral are :

The first angle = 2x = 2 × 20° = 40°

The second angle = 3x = 3 × 20° = 60°

The third angle = 5x = 5 × 20° = 100°

The fourth angle = 8x = 8 × 20° = 160°

Hence,

The measure of all the angles of a quadrilateral are 40°, 60°, 100° and 160°.

Verification :

Substitute all the values in equation (1),

$\implies \angle1 + \angle2 + \angle3 + \angle4 = 360 \degree$

Now we have,

• $\angle1= 40\degree$
• $\angle2=60\degree$
• $\angle3=100\degree$
• $\angle4=160\degree$

So,

$\implies 40 \degree + 60 \degree + 100 \degree + 160 \degree = 360 \degree$

$\implies 100 \degree + 260 \degree = 360 \degree$

$\implies 360 \degree = 360 \degree$

Hence Verified !