Question

Can a triangle have one obtuse and one right angle?

• A. Yes
• B. No
• C. Sometimes
• D. None of these

Answer 1

Answer: (B)

No

$\Rightarrow$ Sum of three interior angle of a triangle is ${180}^o.$

$\Rightarrow$ One obtuse and one right angle by definition mean that there would be one ${90}^o$ angle and other will be more than ${90}^o$.

$\Rightarrow$ Let obtuse angle will be ${91}^o$. So, ${90}^o+{91}^o={181}^o$. That is already too much for a triangle, even before the third angle has been considered.

$\therefore$ A triangle can never have one obtuse and one right angle.