Question

One angle of an isosceles triangle measures 110°. Which other angles could be in that isosceles triangle? Choose all that apply.

1.65 degrees
2.35 degrees
3.10 degrees
4.85 degrees

Answer 1

Therefore the correct option is 2. 35 degree.

`\angle ABC=\angle ACB=35\°`

Explanation:

Consider an Isosceles Triangle, Δ ABC where,

∠BAC = 110°

TO Find:

∠ ABC = ∠ACB = ?

Solution:

For an Isosceles Triangle

Base Angles are equal

∴
`\angle ABC=\angle ACB=x\ (say)`

Now,

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

`\angle A+\angle B+\angle C=180\\\\110+x+x=180\\\therefore 2x=180-110=70\\\therefore x=(70)/(2)=35\°`

Therefore,

`\angle ABC=\angle ACB=35\°`