Question

Which of the following is correct for the figure.

• A. Acute Isosceles Triangle
• B. Obtuse Isosceles Triangle
• C. Right Isosceles Triangle
• D. None of these

Answer 1

The correct option is A Acute Isosceles Triangle

In this triangle,
Let $\angle A={75}^{\circ }$
$\angle B=\angle C$ [Given]
Now,
According to angle sum property,
$\angle A+\angle B+\angle C={180}^{\circ }$
${75}^{\circ }+\angle B+\angle B={180}^{\circ }$ [ $\angle B=\angle C$]
$2\angle B+{75}^{\circ }={180}^{\circ }$
$2\angle B={180}^{\circ }-{75}^{\circ }$
$2\angle B={105}^{\circ }$
$\angle B={52.5}^{\circ }$
Since,
$\angle B=\angle C$
So, $\angle C={52.5}^{\circ }$
All the angles in this triangle are less than ${90}^{\circ }$ and two sides are equal, thus it is an acute isosceles triangle.