Question

Q.No.3:- The Angle of a triangle are in the ratio of 2:4:6. Find the measure of all Angles.​

Answer 1

The measure of all the angles of the triangle are :

• The first angle = 30°
• The second angle = 60°
• The third angle = 90°

Given :

• The ratio of the angles of the triangle = 2 : 4 : 6.

To Find :

• The measure of all the angles of a triangle.

Solution :

Let,

The first angle of the triangle be 2x.

The second angle of the triangle be 4x.

The third angle of the triangle be 6x.

We know that,

Sum of all the angles of the triangle is 180°.

First, we need to find the value of x.

• First angle + Second angle + Third angle = 180°

⇒ 2x + 4x + 6x = 180° -----(1)

⇒ 6x + 6x = 180°

⇒ 12x = 180°

⇒ x = 180° / 12

⇒ x = 90° / 6

⇒ x = 45° / 3

⇒ x = 15°

Hence, the value of x is 15°

So, the measure of all the angles of the triangle are :

★ The first angle = 2x = 2 × 15° = 30°

★ The second angle = 4x = 4 × 15° = 60°

★ The third angle = 6x = 90°

Hence,

The measure of all the angles are 30°, 60° and 90°.

Verification :

From equation (1),

⇒ 2x + 4x + 6x = 180°

We have,

• 2x = 30°
• 4x = 60°
• 6x = 90°

Substitute all the values in equation (1),

⇒ 30° + 60° + 90° = 180°

⇒ 90° + 90° = 180°

⇒ 180° = 180°

Hence Verified !

Answer 2

Answer:

Question

The Angle of a triangle are in the ratio of 2:4:6. Find the measure of all Angles.

To find

Measure of all angle

Solution

We know that sum of all sides of Triangle = 180⁰

Angle in ratio = 2:4:6

Considered angle to be 'x'

Sum of ratio = 2x + 4x + 6x = 12x

In equation

12x = 180

x = 180/12

x = 15 .

1st angle - 2x

2 × 15 = 30⁰

2nd Angle - 4x

4 × 15 = 60

3angle - 6x

= 6 × 15 = 90

Verification

LHS = RHS

180⁰ = 30⁰+60⁰+90⁰

180⁰= 90⁰+90⁰

180⁰ = 180⁰

LHS = RHS

Hence solved

$\small \fbox {Hope it helps}$