ISEE Upper Level Math : How to find an angle in an acute / obtuse isosceles triangle

Study concepts, example questions & explanations for ISEE Upper Level Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #2 : Acute / Obtuse Isosceles Triangles

One of the base angles of an isosceles triangle is \(\displaystyle 42^{\circ}\). Give the measure of the vertex angle.

Possible Answers:

\(\displaystyle 86 ^{\circ}\)

\(\displaystyle 96 ^{\circ}\)

\(\displaystyle 100^{\circ}\)

\(\displaystyle 90^{\circ}\)

\(\displaystyle 98 ^{\circ}\)

Correct answer:

\(\displaystyle 96 ^{\circ}\)

Explanation:

The base angles of an isosceles triangle are always equal. Therefore both base angles are \(\displaystyle 42^{\circ}\).

Let \(\displaystyle x=\) the measure of the third angle. Since the sum of the angles of a triangle is \(\displaystyle 180^{\circ}\), we can solve accordingly:

\(\displaystyle 42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}\)

Learning Tools by Varsity Tutors