Question

Can a triangle have two obtuse angles? Give reason for your answer.

Answer 1

According to the angle sum property, the sum of interior angles of a triangle is ${180}^0$.

$\Rightarrow \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}={180}^0$

An obtuse angle is one whose value is greater than $90°$ but less than $180°$.

Considering two angles $\angle \mathrm{A}$ and $\angle \mathrm{B}$ to be equal to the lowest natural number greater than ${90}^{\mathrm{o}}$, i.e., ${91}^{\mathrm{o}}$

Let $\angle \mathrm{A}={91}^0,\angle \mathrm{B}={91}^0$ and $\angle \mathrm{C}$ be an acute angle

Sum of the angles of a triangles$=91°+91°+\angle \mathrm{C}$

$={182}^0+\angle \mathrm{C}>{180}^0$

Hence, a triangle cannot have two obtuse angles.