The measure of the base angle in an isosceles right triangle is 
.
Further explanation:
A triangle is two dimensional figure which is formed when three non-collinear points are joined. It has three sides, three angles and three edges.
On the basis of the angle a triangle is classified into three categories as follows:
1) Acute angled triangle:
If all the angles of a triangle are less than 
than the triangle is called an acute angled triangle.
2) Obtuse angled triangle:
If any of the angle of a triangle is greater than than the triangle is called obtuse angled triangle.
3) Right angled triangle:
If any one of the angle of the triangle is of than the triangle is called a right angled triangle.
On the basis of the sides of a triangle is classified into three categories as follows:
1) Scalene triangle:
If all the sides of a triangle are unequal or are distinct than the triangle is called a scalene triangle.
2) Equilateral triangle:
If all the sides of triangle are equal in length than the triangle is called an equilateral triangle.
3) Isosceles triangle:
If any two sides of a triangle are equal in length than the triangle is called an isosceles triangle.
In the question it is given that 
is an isosceles right triangle i.e., one of the angle must be of and at least two side of the triangle must be because it is an isosceles triangle.
Consider a triangle as which is right angled at A and the sides AB and AC are the equal sides.
Figure 1 (attached in the end) shows the in which 
and 
.
In an isosceles triangle the angles opposite to the equal sides of the triangle are equal.
Since, is an isosceles triangle and so, the angles opposite to the equal sides are equal.
From figure 1 (attached in the end) it is observed that angle opposite to the side AB is 
and the angle opposite to the side AC is 
.
So, as per the property stated above 
.
Consider the measure of the as 
.
Since, so, 
.
The measure of all the three angles of are 
.
Angle sum property:
Sum of all the interior angles of triangle is always equals to 
.
Apply the angle sum property for .
Therefore, the value of 
is 
.
This implies that the measure of the and is of 
.
Thus, the measure of the base angle in an isosceles right triangle is 
.
Learn more:
1.A problem to determine the equation of line
2.A problem on ray
3.A problem to determine intercepts of a line
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Triangle
Keywords:Triangle, angles, sides, isosceles triangle, scalene triangle, equilateral triangle, right triangle, isosceles right triangle, angle sum property, equal opposite sides, base angle, 90 degrees.
