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°.