Question

If the three angles of a triangle are (x+15°), (6x/5+6°) and (2x/3+30°), prove that the triangle is an equilateral triangle​

Answer 1

Step-by-step explanation:

Three angles are (x+15)°, (6x/5+6)°, (2x/3+30)°

By condition

(x+15)°+(6x/5+6)°+(2x/3+30)° = 180°

(x+15)+(6x/5+6)+(2x/3+30) = 180

x+15+6x/5+6+2x/3+30 = 180

x+15+6x/11+2x/33 = 180

x+6x/11+2x/33+15 = 180

33x+18x+2x/33 = 180

53x/33 = 180

x = 180×33/53

Please do the next by yourself

Answer 2

Step-by-step explanation:

method 1

in equilateral triangle all angles are 60°

angle 1

$angle \: 1 \\ x + 15 = 60 \\ x = 60 - 15 \\ x = 45 \\ \\ angle \: 2 \\ \frac{6x}{5} + 6 = 60 \\ \frac{6x}{5} = 60 - 6 \\ \frac{6x}{5} = 54 \\ 6x = 54 \times 5 \\ x = \frac{54 \times 5}{6} \\ x = 9 \times 5 \\ x = 45 \\ \\ angle \: 3 \\ \frac{2x}{3} + 30 = 60 \\ \frac{2x}{3} = 60 - 30 \\ \frac{2x}{3} = 30 \\ 2x = 30 \times 3 \\ 2x = 90 \\ x = \frac{90}{2} \\ x = 45$

all the x value are 45°

method 2

sum of all angles of a triangle is 180°

$x + 15 + \frac{6x}{5} + 6 + \frac{2x}{3} + 30 = 180 \\ x + \frac{6x}{5} + \frac{2x}{3} + 51 = 180 \\ \\ x + \frac{6x}{5} + \frac{2x}{3} = 180 - 51 \\ \frac{15x + 18x + 10x}{15} = 129 \\ \frac{43x}{15} = 129 \\ 43x = 129 \times 15 \\ x = \frac{129 \times 15}{43} \\ x = 3 \times 15 \\ x = 45$

all the angels are equal to 60° hence it forms an equilateral triangle

hope you get your answer