Question

In an isosceles triangle, the vertical angle is two-fifth of the base angles, then find the measure of the vertical angle.

• A. ${45}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

The correct option is B

${30}^{\circ }$

Let the base angles be $x^{\circ }$. Then, vertical angle $=\left(\frac{2}{5}\right)x$

In the above triangle, $x+x+\left(\frac{2}{5}\right)x={180}^{\circ }$

$2x+\left(\frac{2x}{5}\right)={180}^{\circ }$

$\frac{12x}{5}={180}^{\circ }$

$x=\frac{({180}^{\circ }\times 5)}{12}={75}^{\circ }$

So, vertical angle $=\left(\frac{2}{5}\right)\times {75}^{\circ }={30}^{\circ }$