Download Lesson 11 - Exterior Angle Theorems in Triangles

Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
M1
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 11 - Exterior Angle Theorems in Triangles
Warmup: Regents Prep
1. In the diagram below,
intersects
and
at G and H, respectively, and
What type of triangle is ∆GIH ? (use your reference sheet to help you with that)
If
and
, explain why
.
is drawn such that
.
Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
M1
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 11 - Exterior Angle Theorems in Triangles
Learning Target: I can use the exterior angles theorem to find missing angles
Recall from previous lesson
 The sum of the 3 angle measures of any triangle is__________.
 Each angle of an_____________________________triangle has a measure equal to 60°.
In any triangle, the measure of an _________________ angle is equal to the sum of the measures of the
two ____________________________ angles.
This is known as the _____________________________________________________________.
Example 1
Prove: Why the sum of angle 1 and 2 equal angle 4
Example 2:
Find the measure of angle 𝑥
State the reasons for each answer
Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
M1
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Example 3
Find the measure of angle 𝑏
State the reasons for your answers
Example 4 Set up an appropriate equation to solve for 𝑥 and find the measure of ALL unknown angles in the
diagram.
State the reasons for your answer
Lesson 11
NYS COMMON CORE MATHEMATICS CURRICULUM
M1
M1
GEOMETRY
Name:___________________________________
Period:________ Date:__________
Lesson 11 - Exterior Angle Theorems in Triangles
Classwork
1. Solve for 𝑎
Solve for 𝑎 and 𝑏
2.
Give a reason for each answer
42.
41.
43.
42. 57°
x°
41.
43.
(4x+21)°
(4x+21)°
57°
x°
29°
29°
93°
(2x+8)°
(2x+8)°
x°
93°
x°
(x-10)
(x-
3. In the given triangle below, solve for 𝑥 .
44.
44.
45.
65°
65°
65°
x°
65°
45.
85°
>>
36°
36°
>>
x°
85°
x°
x°
(y+10)°
(y+10)°
4.
46.
z°
>> z°
>>
49.
47.
46.
47.
(4x-13)°
(4x-13)°
2x°
2x°
49.
x°
39
x°
(3x+23)°
(3x+23)°
(3x-18)°
(3x-18)°
65°
65°
2.
43.
57°
NYS COMMON CORE MATHEMATICS CURRICULUM
(4x+21)°
(4x+21)°
M1
M1
Lesson 11
GEOMETRY
Name:___________________________________
(2x+8)°
x°
2x+8)°
(x-10)°
5.
>>
45.
65°
Period:________ Date:__________
(x-10)°
𝑥 = __________
>>
36°
𝑦 = __________
x°
𝑧 = __________
z°
z°
(y+10)°
>>
>>
49.
6.
49.
47.
x°
39°
21°
8)°
x°
65°
𝑥 = __________
39°
𝑦21°
= __________
y°
𝑧 = __________
z°
(3x-18)°
x°
65°
y°
z°
Use the Sum of Triangles and exterior angle theorems to solve for the missing variable
50.
7
851.
x°
52
9
62°
(3x-14)°
32°
(2x+15)°
87°
(x-7)°
51.
50.
(x-9)°
52
x°
62°
(3x-14)°
54.
(2x+15)°
53. 32°
87°
(x-7)°
55.
(x-9)°
55°
55°
29°(y-13)°
29°
>>
x°
(3x-18)°
(x+4)°
(3x-22)°
53.
10
56.
55.
12
(x+4)°
(3x-22)°
57.
(2x+27)°
y°
23°
57.
z°
19°
x°
y°
26°
58.
47°
62°
z°
z°
>>
x°
23°
y°
66°
x°
z°
35°
19°
>>
z°
47°
z°
(y-13)°
35°
z°
z°
58.
(6x-23)°
x°
y°
x°
66°
>>
x°
(3x-18)°
26°
56.
(6x-23)°
(2x+27)°
1154.
62°
x°
34°
y°
34°
y°