Question

How many acute angles does a trapezoid have?

Answer 1

Hint: Since the trapezoid is referred to as a convex quadrilateral having at least one of the pair of sides are parallel. This means if it is a general trapezoid then there are two acute angles and two obtuse angles. However, If the trapezoid is a right-angled trapezoid that is if one of the angles of a trapezoid is a right angle or then there is only one acute angle it would have two right angles and one obtuse angle.

Complete step by step solution:
Case-1: One of the pair of sides is parallel with none of the angle is a right angle
If none of the angles of a trapezoid is right-angled the,

Here as we, one of the pair of the side is parallel and none of the angles is off
There are two acute angles and two obtuse angles.
Case-2: Only one of pair is parallel and have a right angle

From the figure, we can see that, here one of the pairs of sides is parallel and two angles are off.
Since, if one of its angles is then to remain convex quadrilateral one of its other adjacent angles must be.
Case-3: When more than two right angles are in a trapezoid

Since when it has more than two angles to be the right angle then to remain it to be a convex quadrilateral it must be a rectangle that is all four angles must be off.

Hence in this type of trapezoid, none of the angles is acute.

Note:
In this question, according to the definition of a trapezoid that is a convex quadrilateral at least having a pair of side parallel to each other and this makes it is a general case in which many cases may occur and we have discussed all that cases