Question

All the angles are measured in degrees, show that the triangle is isosceles.

Answer 1

Value of degree in a polygon is derived by the formular (n - 2) × 180°
n ==> number of sides

∴ (3 - 2) × 180° = 180°

(4x + 8°) + (5x + 2°) + (6x - 10°) = 180°
Remove the parenthesis

4x + 8° + 5x + 2° + 6x - 10° = 180°
Simplify

15x = 180°
x = 12°

An isosceles triangle has 2 equal angles and sides.

In this case, we check them by the angle.

Substitude x into 4x + 8, 5x + 2 and 6x - 10

1. 4(12°) + 8° = 56°
2. 5(12°) + 2° = 62°
3. 6(12°) - 10° = 62°

Notice 2 and 3 have the same angular value.
∴ ∆ is an isosceles ∆.

Answer 2

The angles in a triangle add up to 180, so its
5x+2+6x-10+4x+8=100, then you combine it, so its 
15x=180, then divide 180 by 15, and you get 12. 
Then insert that into each equation.
4(12)+8= 56
5(12)+2= 62
6(12)-10= 62
They all add up to 180 and two of the angles have the same measure, which makes it an isosceles triangle.