Question

the angles of a triangle are (2x+30)°,(3x-110)° and (5/2x+20)° . find the value of x​

Answer 1

Answer:

Sum of all angles of triangle = 180

(2x+30)° + (3x-110)° + (5/2x+20)° = 180°

2x+30+3x-110+5/2x+20 = 180

2x+3x+5/2x = 180 - 30 + 110 - 20

15/2x = 240

x = 240*2/15

x = 32°           [ANSWER]

Answer 2

since

$2x + 30 \\ 3x - 110 \: \: and \\ \frac{5}{2} x + 20$

are angles of a triangle

$2x + 30 + 3x - 110 + \frac{5}{2}x + 20 = 180$

... (angle sum property of a triangle)

$multiplying \: throughout \: by \: 2 \\ we \: get \\ \\ 4x + 60 + 6x - 220 + 5x + 40 = 360 \\ 4x + 6x + 5x + 60 + 40 - 220 = 360 \\ 15x - 120 = 360 \\ 15x = 360 + 120 \\ 15x = 480 \\ x = \frac{480}{15} \\ x = 32$