Question

If the equal angles of an isosceles triangle measures ${40}^{\circ }$each, then measure of the third angle is ____

• A. ${50}^{\circ }$
• B. ${60}^{\circ }$
• C. ${70}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is D

${100}^{\circ }$

Finding the measure of the third angle:

We know that in an Isosceles Triangle, two opposite sides and their corresponding two angles are equal.

Let the third angle be $"x"$

$$\begin{gathered} {40}^{\circ }+{40}^{\circ }+x^{\circ }={180}^{\circ }(anglesumpropertyoftriangle) \\ \Rightarrow {80}^{\circ }+x^{\circ }={180}^{\circ } \\ \Rightarrow x^{\circ }={180}^{\circ }-{80}^{\circ } \\ \Rightarrow x^{\circ }={100}^{\circ } \end{gathered}$$

Hence, the third angle of an isosceles triangle is $100°$.

Hecne, option (D) is the correct option.