Question

In triangle ABC, angle A= x+20,
angle B= 2(x-10) and angle C= 3x/2.
Show that the triangle is an equilateral triangle.

Answer 1

Answer:

$\bold{sum \: of \: all \: sides \: of \: triangle \: = 180 }\\ x + 20 + 2(x - 10) + \frac{3x}{2} = 180 \\ x + 20 + 2x - 20 + \frac{3x}{2} = 180 \\ \frac{2x + 40 + 4x - 40 + 3x}{2} = 180 \\ 2x + 40 + 4x - 40 + 3x = 2 \times 180 \\ 9x = 360 \\ x = \frac{360}{9} = 40 \\ x = 40 \degree \\ \angle \: a \: = x + 20 = 40 + 20 = 60 \degree \\ \angle \: b \: = 2(x - 10) = 2(40 - 10) = 2(30) = 60 \degree \\ \angle \: c \: = \frac{3x}{2} = \frac{3 \times 40}{2} = \frac{120}{2} = 60 \degree \\ \bold{all \: angles \: are \: 60 \degree.} \\ \bold{ \therefore \: it \: is \: an \: equilateral \: triangle.}$

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