1) Sketch an acute angle. Justify your work.
2) Sketch two adjacent angles.
3)Sketch two equal adjacent angles. 4)Sketch two unequal complementary adjacent angles.
5)Sketch two unequal supplementary adjacent angles.
6)Sketch two equal angles and their supplements.
7) Sketch an acute angle and an obtuse angle;their compliments; their supplements.
Answer:
1) An acute angle is any angle that measures less than 90 degrees. For example, a triangle with angles measuring 30°, 60°, and 90° has an acute angle of 30 degrees.
2) Two adjacent angles are angles that share a common vertex and a common side. For example, two angles that share a leg on a straight line can be adjacent angles.
3) Two equal adjacent angles are angles that measure the same number of degrees and share a common vertex and a common side. For example, two angles measuring 45 degrees and sharing a leg can be equal adjacent angles.
4) Two unequal complementary adjacent angles are angles that add up to 90 degrees but measure different amounts. For example, one angle could measure 30 degrees and the other 60 degrees.
5) Two unequal supplementary adjacent angles are angles that add up to 180 degrees but measure different amounts. For example, one angle could measure 60 degrees and the other 120 degrees.
6) Two equal angles and their supplements are angles that measure the same number of degrees as each other and add up to 180 degrees. For example, two 90-degree angles and their supplements of 90 degrees would work.
7) An acute angle could measure 30 degrees and an obtuse angle could measure 120 degrees. Their complements would be 60 degrees and 70 degrees, respectively. Their supplements would be 150 degrees and 60 degrees, respectively.
