Question

the angles of a triangle are in the ratio of 5:6:7. find each angle

Answer 1

5x + 6x + 7x = 180 degree
18x = 180 degree
x= 180/18 degree
x=10 degree
5x=50 degree
6x=60 degree
7x=70 degree

Answer 2

Answer :

The three angles are 50°, 60° and 70°.

Step-by-step explanation:

Given that :

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

To Find :

The measure of each angle.

Solution :

Given ratios :

⇒ 5 : 6 : 7.

Sum of the Ratios :

⇒ 5 + 6 + 7

⇒ 18.

Consider as -

Angle 1 - 'a'

Angle 2 - 'b'

Angle 3 - 'c'

We know that :

$\bigstar\;\boxed{\textsf {Sum Property of Triangle = 180\textdegree }}}$

So,

$\bigstar\;\boxed{\sf a+b+c = 180\textdegree}$

★ Value of 'a' :

$\sf\\\longrightarrow a = \dfrac{5\times 180}{18}\\ \\ \\ \longrightarrow a = \dfrac{5\times 10}{1}\\ \\ \\\longrightarrow a = 50\textdegree$

$\rule{300}{1.5}$

★ Value of 'b' :

$\sf \\\longrightarrow b = \dfrac{6\times 180}{18}\\ \\ \\\longrightarrow b = \dfrac{6\times 10}{1}\\ \\ \\\longrightarrow b = 60\textdegree$

$\rule{300}{1.5}$

★ Value of 'c':

$\sf \\\longrightarrow c = \dfrac{7\times 180}{18}\\ \\ \\\longrightarrow c = \dfrac{7\times 10}{1}\\ \\ \\\longrightarrow c = 70\textdegree$

∴ The three angles are 50°, 60° and 70°.

$\rule{300}{1.5}$

★ Verification :

As we know,

Sum of the all angles of triangle = 180.

So,

$\sf \\\longrightarrow 50 + 60 + 70\\ \\\longrightarrow 120\textdegree$

Hence, Answer is Correct!