Question

Can a triangle have two acute angles why give reasons.

Answer 1

Obtuse angle triangle:

In an obtuse angle triangle, there will be one obtuse angle and two acute angles, and the sum of interior angles of a triangle is equal to ${180}^0$.

For example, let us consider the measure of angles as,

$$\begin{gathered} \angle \mathrm{A}={20}^0\left[\mathrm{Acute}\mathrm{angle}\right] \\ \angle \mathrm{B}={130}^0\left[\mathrm{Obtuse}\mathrm{angle}\right] \\ \angle \mathrm{C}={30}^0\left[\mathrm{Acute}\mathrm{angle}\right] \end{gathered}$$

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

Here,

$\begin{array}{rcl}\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}& =& {20}^0+{130}^0+{30}^0\\ & =& {180}^0\end{array}$

Since the above measures satisfy the angle sum property of the triangle.

Hence, Yes, a triangle can have two acute angles