Question

A triangle cannot have more than _____ obtuse angle.
(a) One
(b) Two
(c) Three
(d) Zero

Answer 1

Hint:Keep in mind that the sum of all three angles of a triangle is equal to ${{180}^{{}^\circ }}$. Also, obtuse angles means the measure of angle greater than ${{90}^{{}^\circ }}$ and less than 180 degree. Based on this fact we will choose the correct option.

Complete step-by-step answer:
It is given in the question to fill the blank with the most appropriate option. A triangle cannot have more than _____ obtuse angle.
We know that the sum of all the three angles of a triangle is equal to ${{180}^{{}^\circ }}$. Now, obtuse angle means that the angle measure is greater than 90 degree. Therefore, the smallest obtuse angle would be 91 degree and will continue as 92,93,94...179 degrees.
If, out of three angles of a triangle, we take one of the angles as 91 degrees. Therefore the sum of the other two would be $180-91=89$ degree, which means that the sum of two angles is 89 degrees.
Since for an angle to be obtuse, it has to be greater than 90 degree. But here, we get the sum of the remaining two angles as 89 degrees. Therefore, both of the angles cannot be an obtuse angle. Therefore only 1 obtuse angle in a triangle is possible. Taking more than one obtuse angle will lead to the sum of all angles of a triangle be greater than 180 degree, which is not possible.
Thus, option a) is correct.

Note: Most of the students confuse the angle names and they mix all the angles with different measurements. This will seriously divert our facts and correct answers and students may tick the wrong answer. Thus, it is recommended to refer to the basic definition of the angles and their names.