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

Answer:

Step-by-step explanation:

Sum of all angles in triangle is 180

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

=> (x + 6x/5 + 2x/3) + 51 = 180

=> 15x+18x+10x/15 = 129

=> 43x/15 = 129

=> x = 129 * 15/43 = 45°

Thus the angles are

Angle 1 = 45 + 15 = 60°

Angle 2  =  (6 * 45/5 + 6)  = 60°

Angle 3 = 2 * 45/3 + 30 = 60°.

Since all the three angles are each equal to 60°, it is an equilateral triangle.