Question

In ∆ ABC , ∠A = 2∠B = 6∠C then find the measure of ∠A.​

Answer 1

Answer :-

We know that,

In a traingle, sum of all angles is 180°.

So,

➩ ∠A + ∠B + ∠C = 180°

Here, we are given that,

➩ ∠A = 2 ∠B

➩ ∠B = ∠A / 2

Also, ∠A = 6 ∠C

➩ ∠C = ∠A / 6

Substituting the value of ∠B and ∠C -

➩ ∠A + ∠B + ∠C = 180°

➩ ∠A + ∠A /2 + ∠A/6 = 180°

➩ (6∠A + 3 ∠A + ∠A) / 6 = 180

➩ 10∠A = 180 × 6

➩ ∠A = 18 × 6

➩ ∠A = 108

Measure of ∠A = 108°

Answer 2

$\huge\sf\color{purple}\underline{\underline{Answer}} :$

$\angle A = 108°$

$\huge\sf\color{purple}\underline{\underline{Given}} :$

$\angle A = 2\angle B = 6\angle C$

$\huge\sf\color{purple}\underline{\underline{Solution}} :$

As we know ,

Sum of three angles of triangle = 180 °

» ∠A + ∠B + ∠C = 180°

» ∠A + ∠A /2 + ∠A/6 = 180°

» (6∠A + 3 ∠A + ∠A) / 6 = 180

» 10∠A = 180 × 6

» ∠A = 18 × 6

$\boxed{ » ∠A = 108}$