what are the base angles of the triangle?

Question

in an isoceles triangle, the bisector of the vertex angle forms an angle of 27 degrees with each leg. what are the base angles of the triangle?

Answer 1

The vertex angle of an isosceles triangle is the non-base angle.  The bisector makes an angle with the two congruent legs.  Since this is an angle bisector, the angles between the side legs and bisector are the same.  If each angle is 27 degrees, then the vertex angle is double that angle.

 

Vertex angle = 2 * (27 degrees)

Vertex angle = 54 degrees

 

 

Then we apply the sum of the angles in a triangle to find the base angles.  The base angles are the same.

 

Subtract 54 degrees from 180 degrees to get 126 degrees. Then divide the result by 2 to get the base angle.

 

Base angle = 126 degrees / 2

Base angle = 63 degrees

Answer 2

Suppose triangle ABC

C is vertex angle

 

the bisector of the vertex angle forms an angle of 27 degrees with each leg

So vertex angle C= 27+27=54

 

 

addition of internal angle of triangle = 180

 

A+B+ C= 180

 

A+ B+ 54=180

 

A+B=126

 

As triangle ABC is isosceles triangle

 

Angle A= Angle B

 

so Angle A= 126/2=63

 

Angle B= 63

 

So base angles are = 63