Lesson on Lines and Angles for a Geometry class

1. All About Angles
November 4th, 2013

2. An angle is the figure defined by a set of
points which is the union of two rays (or
sides), that have the same endpoint called
the vertex (plural: vertices).
You can name an angle several ways:
•By its vertex
•By a point on each ray and the vertex
•By a number

3. Angles have and Interior and an
Exterior.
Angle Name
ÐR, ÐSRT,
ÐTRS, or Ð1

4. Name three of the angles in the diagram.
Possible
answer:
ÐBAC
ÐCAD
ÐBAD

5. Classify each angle as acute, right, or obtuse.
1. ÐXTS
acute
2. ÐWTU
right
3. ÐUTS
4. ÐXTU
straight
obtuse

6. Many pairs of angles
have special
relationships either
because of their
measurements or their
positions.

9. You can find the complement of an
angle that measures x° by
subtracting its measure from 90°, or
(90 – x)°.
You can find the supplement of an
angle that measures x° by
subtracting its measure from 180°,
or (180 – x)°.

10. Find the measure of each of the following.
A. complement of ÐF
90° – 59° = 31°
B. supplement of ÐG
(180 – x)°
180 – (7x+10)° = 180° – 7x – 10
= (170 – 7x)°
(90 – x)°

11. They are also supplementary.
A linear pair are 2 adjacent,
supplementary angles.

12. Another angle pair relationship exists between two
angles whose sides form two pairs of opposite rays.
Vertical angles are two nonadjacent angles formed by
two intersecting lines.
Ð1 and Ð3 are vertical angles, as are Ð2 and Ð4.
Pairs of vertical angles are congruent, or equal in
measure.

13. Name the
pairs of
vertical
angles.
ÐHML and ÐJMK are vertical angles.
ÐHMJ and ÐLMK are vertical angles.

14. Example 1: Two angles are complementary.
The measure of the larger angle is five times
the measure of the smaller angle. Find the
measure of the larger angle.

15. Example 2: The measure of an angle is 20 less
than the measure of its supplement. Find the
measure of the angle.

16. EXIT SLIP
Identify each of the following.
1. A pair of adjacent angles
2. A pair of complementary
angles
3. A pair of supplementary
angles
D E
A B C

17. Homework
Page 24:
#3 and 4
Pages 36-38:
#4, 8a-d, 12, 14, 18a-c, 25