Question

In \( \triangle ABC \), if \( \angle A = x ^{0}, \angle B =3 x ^{0} \) and \( \angle C = y ^{0} \). If \( 3 y -5 x =30 \), then \( \angle B = \) a) \( 60^{\circ} \) b) \( 45^{\circ} \) c) \( 30^{\circ} \) d) \( 90^{\circ} \).

Answer 1

Given: A = x, B = 3x, C = y

∴ Sum of △le = x + 3x + y

180 = 4x + y

⟹180−4x = y

Also,3y − 5x = 30^∘

Subtituting y value,  

∴ 3(180−4x)−5x = 30

∴ x = 30, by solving

∴ y = 180−4×30 = 60

∴ A = 30^∘; B = 90^∘; C = 60^∘