5.6 - Angle Relationships
Mrs. Kelly
EQ
How are angle relationships used to find missing angles?
Geometry Terms
#1
Basic Geometry Terms
Point
Line
Plane
A location on a plane or in space.
A line that goes forever in two directions.
A flat surface that extends indefinitely in all directions.
Line Segment
Ray
Intersecting Lines
A line that has two end points.
A line that goes forever in two directions
Two or more lines that intersect at a point(s).
Parallel Lines
Perpendicular Lines
Two lines that do not intersect.
Two lines that intersect to form a 90° angle.
Angle Terms
Vertex
Transversal
Straight Angle
A point where two or more straight lines meet.
A line that crosses at least two other lines.
A straight line that forms a 180° angle.
180°
Right Angle
Acute Angle
Obtuse Angle
Two lines that form a 90° angle.
Two lines that form less than a 90° angle.
Two lines that form more than a 90° angle.
Acute
Obtuse
Congruent Angles
Adjacent Angles
Corresponding Angles
Two angles that have the same angle.
ABD⩭EBC
Two angles are adjacent if they share a common side and vertex.
ABD is adjacent to DBE.
DBE is adjacent to EBC.
Two lines that are crossed by another line to form matching corners.
1 & 5
2 & 6
3 & 7
4 & 8
70°
70°
A
B
C
D
E
A
B
C
D
E
1 2
3 4
5 6
7 8
Vertical Angles
Complementary Angles
Supplementary Angles
Angles that are opposite each other when two lines cross.
1 & 4
2 & 3
4 & 8
6 & 7
Two lines that add up to 90°.
Two lines that add up to 180°.
1 2
3 4
5 6
7 8
60°
30°
60°
120°
Triangle Terms
Equiangular Triangle
Acute Triangle
A triangle with all equal sides.
A triangle with all acute angles.
60°
60°
60°
70°
70°
40°
Obtuse Triangle
Right Angle
A triangle that has one obtuse angle.
A triangle that has one right angle.
40°
40°
100°
50°
40°
Equilateral Triangle
Scalene Triangle
Isosceles Triangle
A triangle with all equal sides.
A triangle with no equal sides.
A triangle with two equal sides.
60°
60°
60°
8 in.
8 in.
8 in.
4 in.
8 in.
70°
70°
40°
10 in.
6 in.
6 in.
4 in.
Solving Missing Angles
#2
Example #1: Right Angle
Find the value of x and ∠ABD.
x + 15 + 60 = 90
x + 75 = 90
-75 -75
x = 15
∠ABD = 30°
60°
(x+15)°
A
B
C
D
Example #2: Straight Angle
Find the value of x and ∠DBC.
3x + 5 + 2x - 10 = 180
5x - 5 = 180
+5 +5
5x = 185
x = 37
∠DBC = 64°
2x-10
3x+5
A
B
C
D
Example #3: Transversal
Find all missing angles if ∠1 = 120°
∠1 = 120°
∠2 =
∠3 =
∠4 =
∠5 =
∠6 =
∠7 =
∠8 =
1 2
3 4
5 6
7 8
60°
60°
120°
120°
60°
60°
120°
Example #4: Complex Problem
Find the value of x and ∠FOC if ∠FOE = x - 6, ∠EOD = 3x + 8, and ∠COB = 20°.
x - 6 + 3x + 8 = 90
4x + 2 = 90
-2 -2
4x = 88
x = 22
∠FOE = x - 6 = 16°
∠EOD = 3x + 8 = 74°
∠DOC = 90 - 20 = 70°
∠FOC = 16° + 74° + 70° = 160°
Example #5: Basic Triangle
Find the missing angle.
55 + 82 + x = 180
x + 137 = 180
-137 -137
x = 88
x = 43°
Example #6: Complex Triangle
45°
60°
68°
100°
x°
45°
75°
37°
43°
137°