Question

If in an isosceles triangle, each of the base angles is $40°$, then the triangle is:

• A. Right-angled triangle
• B. Acute-angled triangle
• C. Obtuse-angled triangle
• D. Isosceles right-angled triangle

Answer 1

The correct option is C

Obtuse-angled triangle

Explanation for the correct option:

Calculate the third angle:

Let us draw a suitable diagram first.

As given, in the isosceles triangle $△ABC$,

$\angle B=\angle C=40°$

Now, applying the angle sum property in $△ABC$,

$\angle A+\angle B+\angle C=180°$

$\Rightarrow$ $\angle A+40°+40°=180°$

$\Rightarrow$ $\angle A+80°=180°$

$\Rightarrow$ $\angle A=180°-80°$

$\Rightarrow$ $\angle A=100°$

Now, since $\angle A>90°$

So, $\angle A$ is an obtuse angle.

Hence, the triangle is an obtuse-angled triangle, so, option (C) is the correct option.