Question

What will be the measure of each angle of an isosceles triangle if one angle is ${{90}^{\circ }}$ ?

Answer 1

Hint: In the given question we are given an isosceles triangle of which one angle is ${{90}^{\circ }}$and we need to find the remaining two angles. We know that a triangle is said to be isosceles when two sides of the triangle are equal and the third side is different from the two same sides.

Complete step by step solution:
According to the question, we know that we have an isosceles triangle. A triangle is said to be isosceles when two sides of the triangle are equal and the third side is different from the two same sides.
Of the given isosceles triangle one angle is ${{90}^{\circ }}$and we are being asked the remaining two angles of the same triangle.
We know that the sum of all the three angles of the triangle is ${{180}^{\circ }}$. And we know that one angle is ${{90}^{\circ }}$. Therefore, the sum of the remaining two angles is ${{90}^{\circ }}$.
From the property of the isosceles triangle, we know that two angles of the isosceles triangle are the same. Hence, we can say that the remaining two angles of the triangle are of ${{45}^{\circ }}$.
Therefore, the remaining two angles of the triangle are of ${{45}^{\circ }}$.

Note: In such a type of question, we need to know the angle sum property of the triangle. Also, we need to know all types of triangles and their properties so that we can apply the concept and directly evaluate the value of the angles and hence reach the conclusion.