Question

Is △XYZ equilateral, isosceles, or neither? Explain your reasoning. (Make sure to include how/why you know which of these categories the triangle falls into!)

Answer 1

3 equal angles = equilateral triangle

Explanation:

• the sum of the interior angles in a triangle is 180°

2x + 2x + 3x - 30 = 180

7x = 210

x = 210 : 7

x = 30

• find angle Y & Z

2 x 30 = 60°

• find angle x

3 x 30 - 30 = 60

3 equal angles = equilateral triangle

Answer 2

equilateral

Explanation:

You want to know if the given triangle with angles marked (2x)°, (2x)°, and (3x-30)° is equilateral, isosceles, or neither.

Angles

On the face of it, the triangle is at least isosceles, as two angles are marked identically as (2x)°.

When we apply the angle sum theorem, we find ...

(2x)° +(2x)° +(3x -30)° = 180°

7x -30 = 180

7x = 210

x = 30

2x = 2(30) = 60

3x -30 = 3(30) -30 = 60

All of the angles have the same measure, 60°, so the triangle is equilateral.