Question

1. put these numbers in order from least to greatest:
2. which statement about the figure below is true?

a) it has both acute and right angles.
b) it has both acute and obtuse angles.
c) it has both perpendicular and parallel line segments.
d) it has both obtuse angles and perpendicular line segments.

Explanation:

Step1: Recall properties of a parallelogram

A parallelogram has opposite sides parallel. Its angles are either acute and obtuse (sum of adjacent angles is \(180^{\circ}\)). There are no right - angles (unless it is a special parallelogram like a rectangle) and no perpendicular line segments (since perpendicularity implies right - angles).

Step2: Analyze each option

• Option a: A general parallelogram does not have right - angles. So, this option is incorrect.
• Option b: In a parallelogram, adjacent angles are supplementary (\(\angle A+\angle B = 180^{\circ}\)). If \(\angle A\) is acute (\(0^{\circ}<\angle A<90^{\circ}\)), then \(\angle B=180^{\circ}-\angle A\) and \(90^{\circ}<\angle B<180^{\circ}\) (obtuse). So, a parallelogram has both acute and obtuse angles.
• Option c: A parallelogram has parallel line segments (opposite sides are parallel), but no perpendicular line segments (as there are no right - angles in a general parallelogram). So, this option is incorrect.
• Option d: A parallelogram has no perpendicular line segments (as there are no right - angles in a general parallelogram). So, this option is incorrect.

Answer:

B. It has both acute and obtuse angles.