Question

Based off of the diagram below, correctly categorize each of the angles or angle pairs. Some angles or angle pairs go to more than one category. There are a few incorrect answers as well. The incorrect answers DO NOT get categorized.For context, line DH intersects line AB at point E.Line EG is perpendicular to line AB at point E.

Answer 1

First, recall the meaning of right angles, complementary angles, acute angle and obtuse angle.

A right angle is an agle of 90°.

Complementary angles are those which add up to 90°.

An acute angle is an angle of less than 90°.

An obtuse angle is an angle of more than 90° but less than 180°.

Since the angle AEH is equal to 25.5°, then it is an acute angle.

The angle FEH is equal to 101.4°, then it is an obtuse angle.

AEG is equal to 90°, therefore, it is a right angle.

BED&DEG are both less than 90°, so they are acute angles. Also, they add up to 90°, then, they are complementary angles.

BEF is equal to 53°, so, it is an acute angle.

FEH&AEH are not complementary angles, none of them is a right angle, and one is obtuse but the other is acute. So, that pair of angles does not fit on any category.

BEF&BED are both acute angles.

BED is equal to 25.5°, so it is an acute angle.