Question

In a
traingle ABC , c = 3 B =2 A+B then B =?
​

Answer 1

Step-by-step explanation:

☘Answer:-

☘Solution:

If A, B and C are the angles of triangle

∠A + ∠B + ∠C = 180° (1)

Given relation between the angles is,

$∠C \: = \: 3∠B \: = \: 2 \: (∠A \: + \: ∠B)$

Therefore,

$3∠B \: = \: 2 \: (∠A + ∠B)$

$2∠A \: = \: 3 ∠B \: - \: 2∠B$

$2∠A \: = \: ∠B$

$∠A \: = \: \frac{∠B}{2}$

Substitute in equation (1) :-

$\frac{∠B}{2} \: + \: ∠B \: + \: 3∠B \: = \: 180$

$\frac{∠B}{2} \: + \: 4∠B \: = \: 180$

$∠B \: ( \frac{1 + 8}{2} ) \: = \: 180$

$∠B \: \frac{9}{2} \: = \: 180$

$∠B \: \: \frac{180 \: * \: 2}{9} \: = \: 40$

Thus,

$∠C \: = \: 3 \: * \: 40 \: = \: 120$

$∠A \: = \: \frac{40}{2} \: = \: 20$

✿Hence, ∠B is 40°