Question

The measures of angles of a triangle are in the ratio of 5:6:7 . Find the measures.

Answer 1

Answer:

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Answer 2

Measure of all the angles of a triangle are :–

• $\angle1 = 50 \degree$
• $\angle2 = 60 \degree$
• $\angle3 = 70 \degree$

Given :–

• The measure of angles of a triangle are in the ratio = 5 : 6 : 7.

To Find :–

• The measure of all the angles.

Soluyion :–

Let,

The first angle be 5x.

The second angle be 6x.

The third angle be 7x.

We know that,

Sum of all the angles of a triangle = 180°

I.e.,

$\angle1 + \angle2 + \angle3 = 180 \degree$ –––––(1)

So,

$\mapsto 5x + 6x + 7x = 180 \degree$

$\mapsto 11x + 7x = 180 \degree$

$\mapsto 18x = 180 \degree$

$\mapsto x = \cancel\dfrac{180 \degree}{18}$

$\mapsto x = 10 \degree$

Now, we have to find the measure of all the angles.

First angle = 5x = 5 × 10° = 50°

Second angle = 6x = 6 × 10° = 60°

Third angle = 7x = 7 × 10° = 70°

Hence,

The first angle is 50°, the second angle is 60° and the third angle is 70°.

Verification :–

Substitute all the measure of all the angles of a triangle in equation (1),

Here,

• $\angle1 = 50 \degree$
• $\angle2 = 60 \degree$
• $\angle3 = 70 \degree$

$\mapsto 50 \degree + 60 \degree + 70 \degree = 180 \degree$

$\mapsto 110 \degree + 70 \degree = 180 \degree$

$\mapsto 180 \degree = 180 \degree$

Hence Verified !!