1. Line and Angle Relationships
Lesson 6-1
Line and Angle Relationships

2. Definitions Acute Angles – Angles with measures less than 90°.
Right Angles - Angles with a measure of 90.
Obtuse Angles - Angles with measures between 90° and 180°.
Straight Angles – Angles with measures equal to 180.

3. Vertical Angles are opposite angles formed by intersecting lines
Vertical Angles are opposite angles formed by intersecting lines. They are congruent.
Adjacent Angles have the same vertex, share a common side, and do not overlap.
The sum of the measures of complementary angles is 90°.
The sum of the measures of supplementary angles is 180°

4. Examples 1 and 2
Classify each angle or angle pair using all names that apply. 1
m ∠1 is greater than 90°. So, ∠1 is an obtuse angle.
Ex. 1
∠1 and ∠2 are adjacent angles since they have the same vertex, share a common side, and do not overlap. 1 2
Ex. 2
Together they form a straight angle measuring 180°. So, ∠1 and ∠2 are also supplementary angles.

5. Classify each angle or angle pair using all names that apply.b.
60°
30° a. c. 3 4

6. Example 3 In the figure m∠ABC = 90°. Find the value of x. x° 65° A B C
m∠ABD + m∠DBC = 90°
x + 65 = 90
- 65= -65
x = 25

7. Find the value of x in each figure.
38° d. e. x°
150°

8. Definitions
Lines that intersect at right angles are called perpendicular lines.
Two lines in a plane that never intersect or cross are called parallel lines. p q
Symbol:
p q
Symbol: m ⟘ n m n

9. Definitions
A line that intersects two or more other lines is called a transversal. When a transversal intersects two lines, eight angles are formed that have special names.
If two lines cut by a transversal are parallel, then these special pairs of angles are congruent.
transversal 1 2 4 3 5 6 7 8

10. Definitions
Alernate Inerior Angles – Those on opposite sides of the transversal and inside the other two lines are congruent.
Ex. ∠2 ≅ ∠8
Alternate Exterior Angles – Those on opposite sides of the transversal and outside the other two lines, are congruent.
Ex. ∠4 ≅ ∠6
Corresponding Angles - Those in the same position on the two lines in relation to the transversal, are congruent.
Ex. ∠3 ≅ ∠7 1 2 4 3 5 6 7 8

11. Example 4
You are building a bench for a picnic table. The top of the bench will be parallel to the ground. If m∠1 = 148°, find m∠2 and m∠3. 3 2 1
Since ∠1 and ∠2 are alternate interior angles, they are congruent. So, m∠2 = 148°.
Since ∠2 and ∠3 are supplementary, the sum of their measures is 180°. Therefore, m∠3 = 180° - 148° or 32°.