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