Question

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

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Answer 1

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Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\large{\fbox{Angle\:sum\:Property}$

∠A + ∠B + ∠C = 180°

★Assumption :-

∠A = p°

∠B = c°

★Therefore :-

∠C = 180° - (p° + c°)

★Given :-

∠C = 3∠B = 2(∠A + ∠B)

180° - p - c = 3c

= 2(p + c)

p + 4c = 180

2p - c = 0

(p + 4c) + (8p - 4c) = 180°

= 9p = 180°

${\boxed{\sf\:{p=\dfrac{180}{9}}}}$

p = 20°

20 + 4c = 180°

4c = 180° - 20

4c = 160

${\boxed{\sf\:{c=\dfrac{160}{4}}}}$

c = 40°

∠C = 180° - 20° - 40°

∠C = 120

$\large{\fbox{Hence}}$

∠A = 20°

∠B = 40°

∠C = 120°