Question

Are all isosceles triangles acute?

Answer 1

No. There can be an obtuse angle or a right-angle in an isosceles triangle.

Explanation:

No. You can three types of isosceles triangles:

acute-angled isosceles triangle
All the angles are acute and the base angles are equal.

eg: `75°, 75°, 30°" or "50°, 50°, 80°`

right-angled isosceles triangle
One angle is `90°` and the other two are both `45°`

`45°, 45°, 90°" "larr" "` (like one of the usual set squares)

obtuse-angles isosceles triangle
One angle is obtuse and the base angles are equal.

eg: `30°, 30°, 120°" or "25°, 25°, 130°`

Of course there can only be one `90° or` one obtuse angle in a triangle. The other two angles MUST be acute, else the sum would be more than `180°`