Question

The angle measure of the base angles of an isosceles triangle are represented by x and the vertex angle is 3x + 10. Find the measure of a base angle. a. 112° b. 42.5 c. 340 d. 16°​

Answer 1

Note: In option c, it must be 34°​ instead of 340.

Given:

Base angles of an isosceles triangle are represented by x.

The vertex angle is 3x + 10.

To find:

The measure of a base angle.

Solution:

We know that, base angles of an isosceles triangle are equal. So, base angles are x and x.

According to the angle sum property of triangles, the sum of all interior angles of a triangle is 180 degrees.

Using angle sum property of triangles, we get

`x+x+(3x+10)=180`

`5x=180-10`

`5x=170`

Divide both sides by 5.

`x=(170)/(5)`

`x=34`

The measure of base angle is 34 degrees. Therefore the correct option is c.