Download Solve for Unknown Angles—Angles and Lines at a Point

GEOMETRY
Lesson 6 M1
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:_______________________________________
Date:__________________
Lesson 6: Solve for Unknown Angles—Angles and Lines at a Point
Opening Exercise
Exercise 1: Determine the measure of the missing angle in each diagram.
Discussion
⃗⃗⃗⃗⃗ , are
Two angles 𝐴𝑂𝐶 and 𝐶𝑂𝐵, with a common side 𝑂𝐶
𝐶 belongs to the interior of ∠𝐴𝑂𝐵.
if
Draw an example of adjacent angles.
The sum of angles on a straight line is 180° and two such angles are called a linear pair.
Draw an example of a linear pair.
Two angles are called supplementary if the sum of their measures is
complementary if the sum of their measures is
.
; two angles are called
Describing angles as supplementary or complementary refers only to the measures of their angles; the
positions of the angles or whether the pair of angles is adjacent to each other is not part of the definition.
Draw an example of supplementary angles and complementary angles. Both adjacent and non-adjacent.
Lesson 6:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Solve for Unknown Angles—Angles and Lines at a Point
9/29/15
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.31
Example 1 In the figure, line segment 𝐴𝐷 is drawn.
Find the measure of ∠𝐷𝐶𝐸. Show all work.
𝑚∠𝐷𝐶𝐸 =
Example 2
The total measure of adjacent angles around a point is
.
Find the measure of ∠𝐻𝐾𝐼. Show all work.
𝑚∠𝐻𝐾𝐼 =
Example 3
measure.
Vertical angles have
𝑇
𝑆
Find the measure of ∠𝑇𝑅𝑉. Show all work.
𝑚∠𝑇𝑅𝑉 =
𝑅
𝑉
𝑈
Exercise 2
Find the measures of each labeled angle. Give a reason for your solution.
Angle
Angle measure
Reason
a
b
c
d
e
Lesson 6:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Solve for Unknown Angles—Angles and Lines at a Point
9/29/15
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.32
Examples 4 - 15
In the figures below, ̅̅̅̅
𝐴𝐵 , ̅̅̅̅
𝐶𝐷, and ̅̅̅̅
𝐸𝐹 are straight line segments. Find the measure of each marked angle or
find the unknown numbers labeled by the variables in the diagrams. Give reasons for your calculations. Show
all the steps to your solution.
4.
𝑚𝑎 =
5.
𝑚𝑏 =
6.
𝑚𝑐 =
7.
𝑚𝑑 =
Lesson 6:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Solve for Unknown Angles—Angles and Lines at a Point
9/29/15
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.33
8.
mg =
9.
𝑥=
10.
𝑥=
Lesson 6:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
𝑦=
Solve for Unknown Angles—Angles and Lines at a Point
9/29/15
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.34
11.
𝑥=
12.
𝑥=
𝑦=
13.
𝑥=
Lesson 6:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
𝑦=
Solve for Unknown Angles—Angles and Lines at a Point
9/29/15
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.35
14.
𝑥=
𝑦=
𝑥=
𝑦=
15.
Lesson 6:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Solve for Unknown Angles—Angles and Lines at a Point
9/29/15
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.36
Name:________________________________
Date:________________
Geometry M1L6 HW Solve for Unknown Angle Measures
Period:_____________
Relevant Vocabulary
Straight Angle: If two rays with the same vertex are distinct and collinear (i.e., they form a line), then each of the
angles formed by the line is called a straight angle.
Vertical Angles: Two angles are vertical angles (or vertically opposite angles) if their sides form two pairs of
opposite rays.
Find the value of 𝑥 and/or 𝑦 in each diagram below. Show all the steps to your solution.
1.
𝑥=
𝑦=
2.
𝑥=
3.
𝑥=
Lesson 6:
Date:
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
𝑦=
Solve for Unknown Angles—Angles and Lines at a Point
9/29/15
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.37