Q36 of 186 Page 4

In a ΔABC, ∠C = 3 ∠B = 2 (∠A + ∠B). Find the three angles.

∠A = 20°, ∠B = 40°, ∠C = 120°.

We know that, in a triangle , the sum of three angles is 180°

∴ A + B + C = 180° …(a)


According to the question,



On taking II and III, we get


⇒ 3B = 2 (A + B)


⇒ 3B = 2 A + 2 B


⇒ B = 2 A …(i)


Now, on taking I and II, we get


C = 3 B


⇒ C = 3(2 A) (from eq. (i))


⇒ C = 6 A …(ii)


On substituting the value of B and C in Eq. (a), we get


A + 2A + 6A = 180°


⇒ 9A = 180°


⇒ A = 20°


On puuting the value of A = 20° in Eq. (i) and (ii), we get


B = 2 A = 2(20) = 40°


C = 6 A = 6(20) = 120°


Hence, the angles areA = 20°, B = 40°, C = 120°


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