Question

What is the maximum number of obtuse angles that a quadrilateral can have?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C

3

Find the greatest number of obtuse angles that can be found in a quadrilateral.

We know that the sum of a quadrilateral's angles is $360°$.

Similarly, an obtuse angle is one that is greater than ${90}^0$ but less than ${180}^0$.

Minimum obtuse angle = 91⁰

$$\begin{gathered} {91}^{°}\times 3^{°}={273}^{°} \\ {4}^{\mathrm{th}}\mathrm{angle}={360}^{°}-{273}^{°}={87}^{°}(\because {87}^{°}\mathrm{is}\mathrm{acute}\mathrm{angle}) \end{gathered}$$

Thus, a quadrilateral's angles cannot all be obtuse.

Therefore , nearly three angles can be obtuse.

Hence, Option (C) is the correct answer.