In a ΔABC, if ∠A – ∠B = 420 and ∠B – ∠C = 210 , then the measure of ∠B is: (a) 320 (b) 630 (c) 530 (d) 950
Answers
Given : In a ΔABC, if ∠A – ∠B = 42° and ∠B – ∠C = 21° ,
To Find : the measure of ∠B
(a) 32° (b) 63° (c) 53° (d) 95°
Solution:
∠A – ∠B = 42° Eq1
∠B – ∠C = 21° Eq2
Eq1 - Eq2
∠A – ∠B - (∠B – ∠C ) = 42° - 21°
=> ∠A + ∠C - 2 ∠B = 21° Eq3
in a triangle sum of angles = 180°
∠A + ∠C + ∠B = 180°
=> ∠A + ∠C = 180° - ∠B
Substituting in Eq3
=> 180° - ∠B - 2 ∠B = 21°
=> 180° - 3 ∠B = 21°
=> 60° - ∠B = 7°
=> ∠B = 53°
Correct option is (c) ∠B = 53°
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