Geometry: Angles
Measuring, naming, and reasoning about angles
Geometry: Angles
Measuring, naming, and reasoning about angles
Geometry - Grade 6-8
- 1
An angle measures 35 degrees. Classify the angle as acute, right, obtuse, straight, or reflex. Explain your choice.
Compare the angle measure to 90 degrees.
The angle is acute because it measures less than 90 degrees. - 2
An angle measures 118 degrees. Classify the angle as acute, right, obtuse, straight, or reflex. Explain your choice.
The angle is obtuse because it measures greater than 90 degrees and less than 180 degrees. - 3
Use a protractor to measure angle ABC. Ray BA points straight left from point B, and ray BC points up and to the right. Record the angle measure to the nearest 5 degrees.
Place the center of the protractor on point B and line up one ray with 0 degrees.
The angle measure should be about 135 degrees. Answers near 135 degrees are reasonable if measured carefully. - 4
Two angles are complementary. One angle measures 27 degrees. What is the measure of the other angle?
Complementary angles have a sum of 90 degrees.
The other angle measures 63 degrees because complementary angles add to 90 degrees, and 90 - 27 = 63. - 5
Two angles are supplementary. One angle measures 64 degrees. What is the measure of the other angle?
The other angle measures 116 degrees because supplementary angles add to 180 degrees, and 180 - 64 = 116. - 6
Angles x and 72 degrees form a straight line. Write and solve an equation to find x.
Angles that form a straight line are supplementary.
The equation is x + 72 = 180. Solving gives x = 108, so the angle measures 108 degrees. - 7
Two vertical angles are formed by intersecting lines. One angle measures 83 degrees. What is the measure of the vertical angle across from it?
The vertical angle also measures 83 degrees because vertical angles are congruent. - 8
Two intersecting lines create four angles. One angle measures 122 degrees. Find the measures of the other three angles.
Use vertical angles and supplementary angles.
The vertical angle also measures 122 degrees. Each adjacent angle measures 58 degrees because 180 - 122 = 58. The other three angles are 122 degrees, 58 degrees, and 58 degrees. - 9
In a triangle, two angles measure 45 degrees and 65 degrees. What is the measure of the third angle?
The third angle measures 70 degrees because the angles in a triangle add to 180 degrees, and 180 - 45 - 65 = 70. - 10
In a triangle, the angle measures are x degrees, 2x degrees, and 3x degrees. Find the value of x and the measure of each angle.
Set the sum of the three angle expressions equal to 180.
The angles add to 180 degrees, so x + 2x + 3x = 180. This gives 6x = 180, so x = 30. The angles measure 30 degrees, 60 degrees, and 90 degrees. - 11
Lines m and n are parallel. A transversal crosses them. An angle on line m measures 110 degrees. The corresponding angle on line n is labeled y. What is y?
The value of y is 110 degrees because corresponding angles formed by a transversal crossing parallel lines are congruent. - 12
Lines p and q are parallel. A transversal crosses them. An interior angle on one side of the transversal measures 74 degrees. The alternate interior angle is labeled z. What is z?
Alternate interior angles are inside the parallel lines and on opposite sides of the transversal.
The value of z is 74 degrees because alternate interior angles formed by a transversal crossing parallel lines are congruent. - 13
A full turn is 360 degrees. A student turns 90 degrees to the right, then 45 degrees more to the right. How many degrees has the student turned in all, and what type of angle is the total turn?
The student has turned 135 degrees in all because 90 + 45 = 135. The total turn is an obtuse angle because it is greater than 90 degrees and less than 180 degrees. - 14
An angle is 25 degrees more than a right angle. What is the angle measure, and how should it be classified?
A right angle measures 90 degrees.
The angle measures 115 degrees because 90 + 25 = 115. It is an obtuse angle because it is greater than 90 degrees and less than 180 degrees. - 15
Four angles meet at a point. Three of the angles measure 80 degrees, 95 degrees, and 110 degrees. What is the measure of the fourth angle?
The fourth angle measures 75 degrees because angles around a point add to 360 degrees, and 360 - 80 - 95 - 110 = 75.