Lesson 6-1

Line and Angle Relationships

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.

• 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°

Examples 1 and 2

1

Classify each angle or angle pair using all names that apply.

m ∠1 is greater than 90°. So, ∠1 is an obtuse angle.Ex. 1

Ex. 2 1 2

∠1 and ∠2 are adjacent angles since they have the same vertex, share a common side, and do not overlap.Together they form a straight angle measuring

180°. So, ∠1 and ∠2 are also supplementary angles.

Classify each angle or angle pair using all names that apply.

a.

b.

60° 30°

c.

3

4

Example 3In the figure m∠ABC = 90°. Find the value of x.

m∠ABD + m∠DBC = 90°x + 65 = 90 - 65= -65 x = 25

x°65°

A B

C

D

Find the value of x in each figure.

x° 38°

d.

e. x°

150°

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.

Symbol: m n⟘

m

n

p q

Symbol:p q

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

56

78

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

78

Example 4You 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°.