Download Measuring Angles - Montgomery County Schools

Measuring Angles
LESSON 1-6
Additional Examples
Name the angle below in four ways.
The name can be the number between the sides of the angle:
The name can be the vertex of the angle:
3.
G.
Finally, the name can be a point on one side, the vertex, and a point
on the other side of the angle: AGC, CGA.
Quick Check
HELP
GEOMETRY
Measuring Angles
LESSON 1-6
Additional Examples
Find the measure of each angle. Classify each as acute, right,
obtuse, or straight.
Use a protractor to measure each angle.
m 1 = 110
Because 90 < 110 < 180,
m
1 is obtuse.
2 = 80
Because 0 < 80 < 90,
2 is acute.
Quick Check
HELP
GEOMETRY
Measuring Angles
LESSON 1-6
Additional Examples
Suppose that m
1 = 42 and m
ABC = 88. Find m
2.
Use the Angle Addition Postulate to solve.
m
HELP
1+m
2=m
ABC Angle Addition Postulate.
42 + m
2 = 88
Substitute 42 for m
m
2 = 46
Subtract 42 from each side.
1 and 88 for m
ABC.
Quick Check
GEOMETRY
Measuring Angles
LESSON 1-6
Additional Examples
Name all pairs of angles in the diagram that are:
a. vertical
Vertical angles are two angles whose sides are opposite rays.
Because all the angles shown are formed by two intersecting lines,
1 and 3 are vertical angles, and 2 and 4 are vertical angles.
b. supplementary
Two angles are supplementary if the sum of their measures is 180.
A straight angle has measure 180, and each pair of adjacent
angles in the diagram forms a straight angle. So these pairs of
angles are supplementary: 1 and 2, 2 and 3, 3 and 4,
and 4 and 1.
HELP
GEOMETRY
Measuring Angles
LESSON 1-6
Additional Examples
(continued)
c. complementary
Two angles are complementary if the sum of their measures is 90.
No pair of angles is complementary.
Quick Check
HELP
GEOMETRY
Measuring Angles
LESSON 1-6
Additional Examples
Use the diagram below. Which of the following can
you conclude: 3 is a right angle, 1 and 5 are adjacent,
3 5?
You can conclude that 1 and 5 are adjacent
because they share a common side, a common
vertex, and no common interior points.
Although 3 appears to be a right angle, it is not marked with a right
angle symbol, so you cannot conclude that 3 is a right angle.
3 and 5 are not marked as congruent on the diagram. Although
they are opposite each other, they are not vertical angles. So you
cannot conclude that 3 5.
Quick Check
HELP
GEOMETRY