Question

Amrita measured two angles of a triangle which was $\angle A={30}^{\circ }and\angle B={40}^{\circ }$ and she came to know about the type of the triangle. What type of triangle is it?

• A. Acute-angled triangle
• B. Obtuse-angled triangle
• C. Right-angled triangle
• D. None of these

Answer 1

The correct option is B Obtuse-angled triangle

To know about the type of triangle we need to know about the third angle also.
Since, sum of all interior angles of a triangle is ${180}^{\circ }$
$\angle A+\angle B+\angle C={180}^{\circ }$
${30}^{\circ }+{40}^{\circ }+\angle C={180}^{\circ }$
$\angle C={180}^{\circ }-{30}^{\circ }-{40}^{\circ }$
$\angle C={110}^{\circ }$ $\Rightarrow \text{Obtuse angle}$
$\therefore \text{The triangle is an Obtuse angled triangle}$