Question

The vertical angle of an isosceles triangle is 100 find the base angle

Answer 1

We know that an isosceles triangle has two sides of the same length and one side of different length.

The sum of the measures of the angles of the triangle is 180°.

We know the vertical angle of the triangle i.e., 100°.

Let the base angles be x and x since they have the same value.

So we get,

x+x+100=180° (by condition)

2x+100=180°

2x= 180-100

2x=80

x=80/2

x=40°

So the measure of both the base angles are x i.e., 40°.

Answer 2

Consider an isosceles ΔABC such that

AB=AC

Given that vertical angle A is 100°. Given to find the base angles

Since ΔABC is isosceles ∠B=∠C [Angles opposite to equal angles are equal]

And also,

Sum of the interior angles of a triangle = 180°

= angleA+angleB+angle c=180°

=100+2B=180

Therefore 2angle B=180°-100°

=2ANGLE B=80°

Therefore angle B=40°