Question

Which of the following
The angles of triangle are in the ratio 1:2:3 :. Find the angles?​

Answer 1

★ How to do :-

Here, we are given with the ratio of all the angles of a triangle. We are asked to find the value of all the angles of this triangle. We are going to find the value of all the angles by using an other concept called as variables, in which we apply an alphabet after a part of each ratio and then find the value of that variable and the multiply the value of the same variable with each part of ratio to find the value of each angle. So, let's solve!!

$\:$

➤ Solution :-

${\tt \leadsto 1 : 2 : 3 = {180}^{\circ}}$

Insert a variable x to all the part of ratio and also the addition sign.

${\tt \leadsto 1x + 2x + 3x = {180}^{\circ}}$

Add all the numbers having a variable x.

${\tt \leadsto 6x = {180}^{\circ}}$

Shift the number 6 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{180}{6}}$

Simplify the fraction to get the value of x.

${\tt \leadsto x = \cancel \dfrac{180}{6} = 30}$

$\:$

Now, find the value of each angle of the triangle.

Value of ∠1 :-

${\tt \leadsto 1x = 1 \times 30}$

${\tt \leadsto \angle{1} = {30}^{\circ}}$

Value of ∠2 :-

${\tt \leadsto 2x = 2 \times 30}$

${\tt \leadsto \angle{2} = {60}^{\circ}}$

Value of ∠3 :-

${\tt \leadsto 3x = 3 \times 30}$

${\tt \leadsto \angle{3} = {90}^{\circ}}$

$\:$

Verification :-

${\tt \leadsto \angle{1} + \angle{2} + \angle{3} = {180}^{\circ}}$

Substitute the value of angles 1, 2 and 3.

${\tt \leadsto {30}^{\circ} + {60}^{\circ} + {90}^{\circ} = {180}^{\circ}}$

Add all the values in LHS.

${\tt \leadsto {180}^{\circ} = {180}^{\circ}}$

${\tt \leadsto LHS = RHS}$

$\:$

Hence solved !!