Question

group c - angles in parallel lines, including triangles
calculate the size of angle \\(\theta\\). you must use the sum of angles in a triangle in each solution.
state any other angle facts that you use.

1)
\\(\theta\\), \\(74^\circ\\), \\(28^\circ\\)

2)
\\(52^\circ\\), \\(68^\circ\\), \\(\theta\\)

3)
\\(41^\circ\\), \\(\theta\\)

4)
\\(32^\circ\\), \\(116^\circ\\), \\(\theta\\)

5)
\\(47^\circ\\), \\(18^\circ\\), \\(\theta\\)

6)
\\(77^\circ\\), \\(36^\circ\\), \\(\theta\\)

7)
\\(60^\circ\\), \\(120^\circ\\), \\(\theta\\)

8)
\\(135^\circ\\), \\(\theta\\)

9)
\\(65^\circ\\), \\(45^\circ\\), \\(45^\circ\\), \\(\theta\\)

Explanation:

Solve Question 1

Using the Parallel Line Angles and Triangle Angle Sum Theorem knowledge points

$$
LATEXBLOCK0
$$

Solve Question 2

Using the Parallel Line Angles and Triangle Angle Sum Theorem knowledge points

$$
LATEXBLOCK1
$$

Solve Question 3

Using the Parallel Line Angles, Angle Relationships, and Triangle Angle Sum Theorem knowledge points

$$
LATEXBLOCK2
$$

Solve Question 4

Using the Parallel Line Angles, Angle Relationships, and Triangle Angle Sum Theorem knowledge points

$$
LATEXBLOCK3
$$

Solve Question 5

Using the Parallel Line Angles and Triangle Angle Sum Theorem knowledge points

$$
LATEXBLOCK4
$$

Answer:

Question 1

\(\theta = 46^\circ\)

Question 2

\(\theta = 120^\circ\)

Question 3

\(\theta = 82^\circ\)

Question 4

\(\theta = 148^\circ\)

Question 5

\(\theta = 97^\circ\)

Question 6

\(\theta = 139^\circ\)

Question 7

\(\theta = 120^\circ\)

Question 8

\(\theta = 45^\circ\)

Question 9

\(\theta = 110^\circ\)