Question

The angels of a triangle are in the ratio 3:5:7.find the measure of the three angles.​

Answer 1

Working out:

We are given with the ratio of the angles of the triangle. The given ratio is 3:5:7. So, let's consider the angles be in the form of a one variable (let 'x')

Then,

• The angles are 3x, 5x and 7x

According to angle sum property of triangles, the internal angles of a triangle add upto 180°. So, we can write:

$\sf{ \longrightarrow{3x + 5x + 7x = 180 \degree}}$

$\sf{ \longrightarrow{15x = 180 \degree}}$

Dividing 15 from both sides,

$\sf{ \longrightarrow{ \dfrac{15x}{15} = \dfrac{180 \degree}{15} }}$

$\sf{ \longrightarrow{x = 12 \degree}}$

So, Finding the angles:

• First angle = 3x = 36°
• Second angle = 5x = 60°
• Third angle = 7x = 84°

Measure of the three angles are:

$\huge{\boxed{ \purple{ \sf{36, \degree \: 60 \degree \: and \: 84 \degree}}}}$

And we are done !!

Answer 2

Answer :

→ 36° , 60° and 84°

_________________________

Given :

The angles of triangles in ratio of 3:5:7

To Find :

The measure of three angles

Sølution :

• The Angle Sum Property of triangle is 180° .

Now , let the angle be " x " .

=> 3x + 5x + 7x = 180°

=> 15x = 180°

=> x = $\sf \dfrac{180°}{15}$

=> x = 12°

• Value of x is 12°

Now , measure of three angles are :

• 3x = 3(12) = 36°

• 5x = 5(12) = 60°

• 7x = 7(12) = 84°

________________________________

Verification :

= Angle 1 + Angle 2 + Angle 3 = 180°

= 36° + 60° + 84° = 180°

= 180° = 180°

— LHS = RHS , Hence Proved .

_____________________