1. Ch. 10 Geometry: Line and Angle Relationships

2. Vocabulary for angles:
Acute angles: less than 90°
Right angles: 90°
Obtuse angles: more than 90°
Straight angles: 180 °

3. Vocabulary for angles:
Vertical angles: opposite angles form by intersecting lines. Vertical angles are congruent.
So,∠1=∠2; ∠3 =∠4
Complementary angles: sum of angles is 90
∠60° +∠30° =∠90°
Supplementary angles: sum of angles is 180 °
So,∠120° +∠60° =∠180° 1 2 3 4
30°
60°
120 °
60°

4. Line and Angle Relationships
Can you tell their names?
Acute Angle
Vertical Angles
Obtuse Angle
Complementary angles
45°
45° ∠3 ∠1

5. Line and Angle Relationships
Can you tell their names?
Right angles
Straight angles
Supplementary angles
135°
45°
180°

6. Line and Angle Relationships
This is a complementary angle. The sum of angles = 90°. So,
x° + 35° = 90°
x = 90° - 35°
x = 55°
2. Find the missing angles
Example 1:
35° x°

7. Line and Angle Relationships
2. Find the missing angles
Example 2:
This is a supplementary angle. The sum of angles = 180°. So,
45° + x° + 55° = 180°
x = 180°- 55° - 45 °
x = 180° °
x = 80°
45° x°
55°

8. Line and Angle Relationships
2. Find the missing angles
Example 3:
They are a vertical angles. The opposite angles congruent to one another. So,
x° = 75°
y° = 105°
Reason: vertical angles
105°
75° x° y°

9. Line and Angle Relationships
2. Find the missing angles
Your turn:
x° + 60° = 90°
x = 90° - 60°
x = 30° x°
60°

10. Line and Angle Relationships
2. Find the missing angles
Your turn:
x° = 120°
y° = 60°
Reason: vertical angles
60°
120° x° y°

11. Ch. 6-1 Line and Angle Relationships
2. Find the missing angles
Your turn:
This is a supplementary angle. The sum of angles = 180°. So,
80° + x° + 35° = 180°
x = 180°- 80° - 35 °
x = 65° x°
80°
35°

12. Vocabulary for lines:
Perpendicular Lines: Lines intercept at right angles. Symbol: e.g. m n
Parallel Lines: Lines never intersect or cross. Symbol: II
Transversal: A line that intersects 2 or more lines.
Right angle symbol indicates the lines are perpendicular.
The arrowheads indicate that two lines are parallel.

13. Vocabulary for lines: Alternate Interior Angles are congruent
What happen when a transversal passes through two parallel lines?
Alternate Interior Angles are congruent
So, x°= y°
2. Alternate Exterior Angles are congruent
So, a°= b°
3. Corresponding angles are congruent.
So, s°= t ° x° y° a° b°
s °
t °

14. Line and Angle Relationships
3. Find the angle measure
Example 1 (2001 FCAT):
Tyrone is building a picnic table
to be used in a local park. An end
view of the picnic table is shown
below. Tyrone needs to know the
measure of angle x. The top of
the table will be parallel to the
ground. One side of each leg will
meet the ground at a 145° angle.
What is the measure, in degrees,
of angle x?
A. 35 ° B. 45 ° C. 145 ° D. 180 °
145° x°
Angle x ° and angle 145 ° are alternate interior angles. They are congruent. So, x ° = 145 °
C is the answer

15. Line and Angle Relationships
1. Find ∠2 if ∠1 = 63°
∠2 and ∠1 are
corresponding angles.
Their angles are congruent.
So, ∠2 = ∠1 = 63 °.
2. Find ∠3 if ∠8 = 100°
∠3 and ∠8 are alternate exterior angles. Their angles are congruent. So, ∠3 = ∠8 = 100°
3. Find ∠4 if ∠7 = 82°
∠4 and ∠7 are supplementary angles. The sum of their angles equal to 180°,
So, ∠4 + ∠7 = 180°
∠4 + 82° = 180°
∠4 = 180° – 82°
∠4 = 98°
3. Find the angle measure
Your turn:
1. Find ∠2 if ∠1 = 63°
2. Find ∠3 if ∠8 = 100°
3. Find ∠4 if ∠7 = 82° 3 6 4 7 1 5 2 8