Download Directions: Set up an equation to solve each problem below.

Name: ____________________________________ Date: __________________________
Geometry Unit 1 Day 3: Unknown Angles in Transversals and Parallel Lines
Goal: I can use angle pairs in HW:
Upcoming Events:
parallel lines to find missing 1-3 Transversal Angles
angles.
Directions: Use your Unit 1 Reference Guide to help you answers the questions below.
1) Use the diagram below to find the measure of ∠𝑪𝑶𝑭. 𝑨𝑩 and 𝑪𝑫 are straight lines.
a) 30
b) 90
c) 52
d) 96
2) In the diagram above which is a pair of vertical angles?
a) ∠COF & ∠EOD
b) ∠AOF & ∠FOB
c) ∠AOC & ∠DOB
d) ∠AOE & ∠DOF
3) Which of the following represents a same side interior angle pair with the 48° angle?
a)
b)
c)
d)
Use the diagram and work below to answer questions 4 & 5.
Statements
Reasons
y + x + y – x = 180
#4
y = 90
2x = y – x
Angles on a line equal 180
Combine Like Terms
Division
#5
2x = 90 – x
Substitution
3x = 90
Addition
x = 30
Division
4) What statement best fills in the blank labeled #4?
a) 2y = 180
b) 2y – 2x = 180
c) 2y = 90
5) Which reason best fills in the blank labeled #5?
a) Subtraction
b) Angles around a point = 360
c) Vertical angles are congruent
d) Angles on a line = 180
d) y = 90
Name: ____________________________________ Date: __________________________
Geometry Unit 1 Day 3: Unknown Angles in Transversals and Parallel Lines
Discussion
Given a pair of lines 𝐴𝐵 and 𝐶𝐷 in a plane (see the diagrams below), a third line 𝐸𝐹 is called a transversal if it
intersects 𝐴𝐵 at a single point and intersects 𝐶𝐷 at a single but different point. The two lines 𝐴𝐵 and 𝐶𝐷 are
parallel if and only if the following types of angle pairs are congruent or supplementary:

Corresponding Angles (corr.) are equal
▪ Same Side Interior Angles (ss. Int.) add to 180°
Angle Pairs:____________________________

Alternate Exterior Angles (alt. ext.) are equal
Angle Pairs:____________________________

Alternate Interior Angles (alt. int.) are equal
Angle Pairs:____________________________
Angle Pairs:____________________________

Vertical Angles (Vert.) are equal
Angle Pairs:_________________________________________
An _________________________________is sometimes useful when
solving for unknown angles. In this figure, we can use the dotted
auxiliary line to find the measures of ∠𝑒 and ∠𝑓 . Then we can use ∠𝑒
and ∠𝑓 to find the measure of ∠𝑊.
* Use your “Z”s to find the alternate interior angles.
Statements
Reasons
Exercises: Show work by CLEARLY labeling all angles in the diagram to find the missing angles. Make sure to
draw in the auxiliary line and highlight your “Zs”
1.
∠𝑔 = _________
2. An architect is inputting measurements into design software of an existing building. The shaded region is
not accessible to measure. How can the architect determine the measure of angle i?
∠𝑖 = __________
3.
∠𝑛 = _______
4.
∠𝑝 = _______
∠𝑞 = _______
5.
∠𝑟 = __________
6.
∠𝑎 = ________
7.
∠𝑏 = ______
∠𝑐 = ______
8.
∠𝑓 = ________
Name: ____________________________________ Date: __________________________
Geometry A U2D7: Transversal Angles HOMEWORK 1-2
In each exercise below, find the unknown (labeled) angles. Give reasons for your solutions.
1.
Statements
Reasons
If lines are parallel alternate exterior angles are
equal.
c + 53 = 180
∠a = 53°
2.
Statements
Reasons
∠m =
∠j =
j + k + 46 = 180
Substitution
Directions: Show work by CLEARLY labeling all angles in the diagram to find the missing angles. Make sure to
draw in the auxiliary line and highlight your “Zs”
3.
∠𝑑 = ___________
4.
∠𝑒 = ____________
∠𝑓 = ___________
5.
∠ℎ = __________
6.
∠𝑑 = ________
∠𝑒 = ________
Directions: Set up an equation to solve each problem below.
S
R
7.
3d - 24
12c – 8
U
&
2d + 4
3c + 19
Y
V
V
Find
W
X
8.
Z
T
= ______ &
= ______ &
= ______
Find
= _______
&
= ______ &
= _______
= _______ &
= ______