Question

An isosceles triangle has an angle that measures 40°. Which other angles could be in that isosceles triangle? Choose all that apply. 70, 100,80,40

Answer 1

Given:

An isosceles triangle has an angle that measures 40°.

To find:

The other possible angles of the triangle.

Solution:

Case 1: 40° is the measure of base angle of isosceles triangle.

Then, the other base angle is 40°.

Let x be the measure of third angle.

The sum of all interior angles of a triangle is 180 degrees. So,

`x+40^\circ+40^\circ=180^\circ`

`x=180^\circ-40^\circ-40^\circ`

`x=100^\circ`

So, the possible angles are 40° and 100°.

Case 2: 40° is the measure of vertical angle of isosceles triangle.

Let y be the measure of base angles, then

`y+y+40^\circ=180^\circ`

`2y=180^\circ -40^\circ`

`y=(140^\circ)/(2)`

`y=70^\circ`

So, the possible angles are 40° and 70°.

Therefore, the correct options are A, B and D.