Question

In a ΔABC, if ∠A – ∠B = 420

and ∠B – ∠C = 210

, then the measure of ∠B is:​

Answer 1

Answer:

angle B = 53°.

Step-by-step explanation:

A+B+C= 180°

180-42+21=159°

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Answer 2

The measure of ∠B is 53°

Given :

In a ΔABC, if ∠A – ∠B = 42° and ∠B – ∠C = 21°

To find :

The measure of ∠B

Solution :

Step 1 of 2 :

Write down the given data

In a ΔABC,

∠A – ∠B = 42° - - - - - (1)

∠B – ∠C = 21° - - - - - - (2)

Step 2 of 3 :

Find sum of three angles

We know that for a triangle ΔABC

∠A + ∠B + ∠C = 180°

⇒ ∠A + ∠C = 180° - ∠B - - - - - (3)

Step 3 of 3 :

Find measure of ∠B

Equation 1 - Equation 2 gives

∠A - 2∠B + ∠C = 21° - - - - (4)

From Equation 3 and Equation 4 we get

180° - ∠B - 2∠B = 21°

⇒ 3∠B = 159°

⇒ ∠B = 53°

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