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Pair of Linear Equations in Two Variables
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28/05/2021 11:17 am
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In a ∆ABC, ∠ C = 3 ∠B = 2 (∠A + ∠B). Find the three angles.
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28/05/2021 11:20 am
Given,
∠C = 3 ∠B = 2(∠B + ∠A)
∠B = 2 ∠A+2 ∠B
∠B = 2 ∠A
∠A – ∠B = 0 ..........(i)
We know, the sum of all the interior angles of a triangle is 180°.
Thus, ∠A +∠B+ ∠C = 180°
∠A + ∠B +3 ∠B = 180°
∠A + 4 ∠B = 180° ..........(ii)
Multiplying 4 to equation (i) , we get
8∠A – 4∠B = 0 ...........(iii)
Adding equations (iii) and (ii) we get
9 ∠A = 180°
∠A = 20°
Using this in equation (ii), we get
20° + 4∠B = 180°
∠B = 40°
3∠B =∠C
∠C = 3 x 40 = 120°
Therefore, ∠A = 20°
∠B = 40°
∠C = 120°