Question

How many acute angles can an isosceles triangle have?

Answer 1

Hint: Triangle types are defined by angle and length properties. It is possible to calculate the missing angles of a triangle easily if you know what type it is. The sum of angles in any triangle is ${180^\circ}$. On a diagram, equal sides of a triangle have one small line or dash drawn on each side.

Complete step-by-step solution:
Definition: (Isosceles triangle)
An isosceles triangle is a triangle that has two sides of equal length.
Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
The two equal sides are called the legs and the third side is called the base of the triangle.
The other dimensions of the triangle such as its height, area, and perimeter can be calculated by simple formulas from the lengths of the legs and base.
What is Acute angle?
An acute angle is less than${90^ \circ }$
How many acute angles can an isosceles triangle have?
All isosceles triangles have two acute angles. Because the sum of the interior angles of a triangle must be ${180^ \circ }$ .Acute angle is less than $90$ degrees. Any two angles of a triangle must have a sum of less than $180$ degrees.
We require two equal angles for any isosceles triangle. The sum of these two must be less than $180$ degrees so any one of these two angles must be less than $90$ degrees, meaning “acute”
Diagram:

Note: Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base.
The two angles opposite the legs are equal and are always acute, so the classification of triangle as acute, right or obtuse depends only on the angle between its two legs.
Area of isosceles triangle $ = \dfrac{b}{2}\sqrt {{a^2} - \dfrac{{{b^2}}}{4}} $
Perimeter of isosceles triangle $ = 2a + b$