GEOMETRY
Measuring and Describing Pairs of Angles
LESSON 1-5 & 1-6
GEOMETRY
Angle
An angle whose measure is larger than 0° but less than 90°.
Measuring Angles LESSON 1-6
Vocabulary Review:
An angle is a figure formed by two rays (sides) with a common endpoint.
Acute Angle
An angle whose measure is 90° exactly. Right Angle
An angle whose measure is larger than 90° but less than 180°. Obtuse Angle
sides
vertex
GEOMETRY
Straight Angle
Two angles whose sides are opposite rays.
Measuring Angles LESSON 1-6
Vocabulary: New
An angle whose measure is 180° exactly.
Vertical Angles
Two angles with a common side, a common vertex and no common interior points.
Adjacent Angles
GEOMETRY
Congruent angles
A ray that cuts an angle into congruent angles.
Measuring Angles LESSON 1-6
Vocabulary: New
Angle measures that are same.
Bisector of an angle
Two angles with a common side, a common vertex and they form 180°.
Linear pair of angles
∠3≅∠4m∠3=m∠4
∠3≅∠4m∠3=m∠4
m∠1+m∠2 =180
GEOMETRY
Complementary Angles
Two angles whose measures add up to 180°.
Measuring Angles LESSON 1-6
Vocabulary
Two angles whose measures add up to 90°.
Supplementary Angles
m∠1+m∠2 = 90
m∠3+m∠4 =180
GEOMETRY
The name can be the vertex of the angle:
Finally, the name can be a point on one side, the vertex, and a point on the other side of the angle:
The name can be the number between the sides of the angle:
Measuring Angles
a) Name the angle below in four ways. b) Use a protractor to determine the measure.
∠3
∠G
∠CGA∠AGC
GEOMETRY
The measure of the angle is 30°, and it is acute so the answer is A.
Measuring Angles LESSON 1-6
You Try #1
GEOMETRY
Measuring Angles LESSON 1-6
Postulate & Examples
You can use the angle addition postulate to set up equations for missing angles.
GEOMETRY
Use the Angle Addition Postulate to solve.
m 1 + m 2 = m ABC Angle Addition Postulate.
42 + m 2 = 88 Substitute 42 for m 1 and 88 for m ABC.
m 2 = 46 Subtract 42 from each side.
Suppose that m 1 = 42 and m ABC = 88. Find m 2.
Measuring Angles LESSON 1-6
Example 2:
GEOMETRY
Measuring Angles LESSON 1-6
You Try #2
Use the angle addition postulate.
A
B C
D
4. In the figure find
137 ,m ABC∠ = ° 43 ,m DBC∠ = °.m ABD∠
43 13794
m ABD m DBC m ABCx
m ABC
∠ + ∠ = ∠
+ =
∠ = °
43°
137°
GEOMETRY
Measuring Angles LESSON 1-6
You Try #3
J
K L
M12x + 15
5x+12 Find the value of x
In the figure and
5 12,m MKL x∠ = + 12 15,m JKM x∠ = +20 9,m JKL x∠ = +
5 12 12 15 20 917 27 20 9
3 186
m JKM m MKL m JKLx x x
x xxx
∠ + ∠ = ∠
+ + + = +
+ = +
=
=
20x + 9
GEOMETRY
Apply the definition of supplementary angles to find the value of x.
Two supplementary angles have measures of (4x+36) and (2x-12). Find the value of x, each angle and justify your steps.
(4x+36) (2x-12)
Example 3:
GEOMETRY
Proving Angles Congruent LESSON 2-5
You Try #4
Two complementary angles have measures of (5x-10) and (6x-10). Find the value of x and justify your steps.
GEOMETRY
Name all pairs of angles in the diagram that are: a. vertical
Vertical angles are two angles whose sides are opposite rays.
Two angles are supplementary if the sum of their measures is 180. :
Measuring Angles LESSON 1-6
c. complementary Two angles are complementary if the sum of their measures is 90. No pair of angles is complementary.
d. adjacent
b. supplementary
4&2,3&1 ∠∠∠∠
1&4,4&3,3&2,2&1 ∠∠∠∠∠∠∠∠
1&4,4&3,3&2,2&1
∠∠∠∠
∠∠∠∠
Example 4:
GEOMETRY
Use the diagram below. Which of the following can you conclude to be true?
Measuring Angles LESSON 1-6
You Try #5
A ∠3 is rightB ∠1&∠5 are adjacentC ∠2&∠4 are verticalD ∠3&∠5 are vertical