Question

An isosceles triangle has an angle that measures 42 degrees. What other angles could be in that isosceles triangle?

Answer 1

See explanation.

Explanation:

If a triangle is isosceles then it has 2 identical angles and the third different one. So in the given example we have to check 2 cases:

I. The given angle is opposite to the base

Then we have the angles: `42,x,x`, where `x` is the angle at the base.

To calcu;late `x` we use the property saing that the sum of angles in any triangle is equal to 180.

`2x+42=180`

`2x=138`

`x=69`

So the angles are: `42^o,69^o` and `69^o`

II. The given angle is one of the angles at the base

Then the angles are `42,42,x`. We have to calculate the angle opposite to the base. As before we use the sum of angles identity:

`2*42+x=180`

`84+x=180`

`x=96`

The angles are: `42^o,42^o` and `96^o`