Question

One of the base angles of an isosceles triangle is equal to ${45}^{\circ }$. Find the vertex angle of the triangle.

• A. ${53}^{\circ }$
• B. ${76}^{\circ }$
• C. ${54}^{\circ }$
• D. ${74}^{\circ }$

Answer 1

The correct option is D

${74}^{\circ }$

Let $\Delta$ ABC be the isosceles triangle with one of base angle 45${}^{\circ }$ as shown below.

Here, vertex angle $=\angle A$

By angle sum property, $\angle A+\angle B+\angle C={180}^{\circ }$
In Isosceles triangle, base angles are equal. Hence two angles will be equal i.e $\angle B=\angle C={45}^{\circ }$

So, $\angle A={180}^{\circ }-(\angle B+\angle C)$

= ${180}^{\circ }-({45}^{\circ }+{45}^{\circ })$

= ${180}^{\circ }-{90}^{\circ }$

= ${90}^{\circ }$