3.10 Worksheet #1 – Applying Triangle Relationships NAME: ________________________ 1 1. Determine the measure of the angle. a) m∠A = ________ b) m∠C = ________ B
B
d) m∠A = ________ B
60°
B
48°
99°
118°
C
65°
41°
C
A
c) m∠C = ________ A
A
C
A
C
2. Determine the measure of the angles. a) m∠1 = _______ m∠2 = ______ b) m∠1 = _______ m∠2 = ______ c) m∠1 = _______ m∠2 = ______ m∠3 = _______ m∠3 = _______ 1
2
64°
27°
76°
1
2
1
3
2
68°
3
3. Determine the missing information. a) x = _______ m∠A = _________ b) x = _______ m∠B = _________ c) x = _______ m∠A = _________ B
B
B
68°
4x
2x
3x - 3
A
3x
2x
A
2x
3x + 5
C
A
C
4. An exterior angle is formed between a side and the extension of a side. It will always be a linear pair with an internal angle. In the diagram below, ∠ 4 is the exterior angle. The exterior angle theorem states that the EXTERNAL ANGLE IS EQUAL TO THE SUM OF THE TWO REMOTE ANGLES. The remote angles are those interior angles that are not adjacent to the exterior angle so in this case ∠ 1 & ∠ 2 are the remote angles. C
B
m∠1 + m∠2 = m∠4, Explain why this would be true. 1
2
A
4
3
C
3.10 Worksheet #1 – Applying Triangle Relationships 5. Determine the missing information. 2 a) m∠1 = ______ m∠3 = ______ B
b) m∠1 = ______ m∠3 = ______ B
c) m∠1 = ______ m∠3 = ______ 98°
40°
1
3
49°
18°
124°
A
C
A
3
1
3
1
C
165°
6. Find the value of x a) x = ____________ b) x = ____________ 2x - 2
c) x = ____________ x
3x - 17
x
x
x+5
d) x = ____________ x + 40
2x - 5
e) x = ____________ f) x = ____________ E
47°
x
B
42°
48°
64°
81°
x
h) x = ____________ g) x = ____________ 52°
F
82°
D
C
i) x = ____________ 121°
x
x
A
56°
59°
x
x
65°
82°