Answer. Answer: The measure of a base angle of an isosceles right triangle is 45 degrees. In any triangle, the measure of all three angles equals 180 degrees.

Whether an isosceles triangle is acute, right or obtuse depends only on the angle at its apex. In Euclidean geometry, the base angles can not be obtuse (greater than 90°) or right (equal to 90°) because their measures would sum to at least 180°, the total of all angles in any Euclidean triangle.

Identifying isosceles triangles An isosceles triangle has two equal sides (or three, technically) and two equal angles (or three, technically). The equal sides are called legs, and the third side is the base. The two angles touching the base (which are congruent, or equal) are called base angles.

Sum of all angles in a triangle in always 180 degree. ✏So, first is 90 degree as it is right angled triangle. Since the measure of equal angles is 45 degree.

The measure of a base angle of an isosceles right triangle is 45 degrees. In any triangle, the sum of all three angles equals 180 degrees.

ninety degree angle

To prove the Base Angles Theorem, we will construct the angle bisector through the vertex angle of an isosceles triangle. By constructing the angle bisector, /begin{align*}/overline{EG}/end{align*}, we designed two congruent triangles and then used CPCTC to show that the base angles are congruent.

An Isosceles Triangle has the Following Properties:

• It has two sides of equal length.
• The angles opposite to equal sides are equal in measure.
• The altitude from vertex A to the base BC is the perpendicular bisector of the base BC.
• The altitude from vertex A to the base BC is the angle bisector of the vertex angle ∠ A.