Angles and Parallel Lines

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Question 1 of 4

1. Question
Find the value of $x$ $x$
- $x =$ $x=$ (58) $°$ $°$
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Vertically Opposite Angles

Corresponding Angles

Co-Interior Angles

Co-Interior Angles are when two angles have a sum of $180 °$ $180°$ .

Vertically Opposite Angles are equal.

To solve for $x$ $x$ , get the supplementary angle of $122 °$ $122°$ .

First, we can see from the diagram that $122 °$ $122°$ and $∠ A C D$ $/_ACD$ are co-interior angles, which add to $180 °$ $180°$

Since co-interior angles add to $180 °,$ $180°,$ add the angle measures and set their sum to $180 ° .$ $180°.$ Then, solve for the value of $∠ A C D$ $/_ACD$ .

$∠ A C D + 122$ $/_ACD+122$ $=$ $=$ $180$ $180$

$∠ A C D + 122$ $/_ACD+122$ $- 122$ $-122$ $=$ $=$ $180$ $180$ $- 122$ $-122$ Subtract $122$ $122$ from both sides

$∠ A C D$ $/_ACD$ $=$ $=$ $58 °$ $58°$

Finally, we can see that angle $∠ A C D$ $/_ACD$ is vertically opposite to angle $x$ $x$

Since vertically opposite angles are equal, $∠ x = 58 °$ $/_ x=58°$

$∠ x = 58 °$ $/_ x=58°$

Question 2 of 4

Find the value of

a

$a$

$a =$ $a=$ (100) $°$ $°$

Question 3 of 4

3. Question
Find the value of $x$ $x$
- $x =$ $x=$ (85) $°$ $°$
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Alternate Angles

Corresponding Angles

Co-Interior Angles

Co-Interior Angles are when two angles have a sum of $180 °$ $180°$ .

Alternate Angles are equal.

To solve for $x$ $x$ , get the supplementary angle of $95 °$ $95°$ .

First, we can see from the diagram that $95 °$ $95°$ and $∠ B D C$ $/_BDC$ are co-interior angles, which add to $180 °$ $180°$

Since co-interior angles add to $180 °,$ $180°,$ add the angle measures and set their sum to $180 ° .$ $180°.$ Then, solve for the value of $∠ B D C$ $/_BDC$ .

$∠ B D C + 95$ $/_BDC+95$ $=$ $=$ $180$ $180$

$∠ B D C + 95$ $/_BDC+95$ $- 95$ $-95$ $=$ $=$ $180$ $180$ $- 95$ $-95$ Subtract $95$ $95$ from both sides

$∠ B D C$ $/_BDC$ $=$ $=$ $85 °$ $85°$

Finally, we can see from the diagram that $∠ B D C °$ $/_BDC°$ and $x$ $x$ are alternate angles, which means they are equal

Therefore, $∠ x = 85 °$ $/_ x=85°$

$∠ x = 85 °$ $/_ x=85°$
Question 4 of 4

4. Question
Find the value of $k$ $k$
- $k =$ $k=$ (250) $°$ $°$
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Alternate Angles

Corresponding Angles

Co-Interior Angles

Co-Interior Angles are when two angles have a sum of $180 °$ $180°$ .

To solve for $k$ $k$ , add the co-interior angles of $50 °$ $50°$ and $60 °$ $60°$ .

First, add an imaginary line to the figure in a way that it is parallel to the two other parallel lines.

Now, we can see from the diagram that $50 °$ $50°$ and $x$ $x$ are co-interior angles, which add to $180 °$ $180°$

Since co-interior angles add to $180 °,$ $180°,$ add the angle measures and set their sum to $180 ° .$ $180°.$ Then, solve for the value of $x$ $x$ .

$x$ $x$ $+ 50$ $+50$ $=$ $=$ $180$ $180$

$x$ $x$ $+ 50$ $+50$ $- 50$ $-50$ $=$ $=$ $180$ $180$ $- 50$ $-50$ Subtract $60$ $60$ from both sides

$x$ $x$ $=$ $=$ $130 °$ $130°$

Next, we can also see from the diagram that $60 °$ $60°$ and $y$ $y$ are co-interior angles, which add to $180 °$ $180°$

Since co-interior angles add to $180 °,$ $180°,$ add the angle measures and set their sum to $180 ° .$ $180°.$ Then, solve for the value of $y$ $y$ .

$y$ $y$ $+ 60$ $+60$ $=$ $=$ $180$ $180$

$y$ $y$ $+ 60$ $+60$ $- 60$ $-60$ $=$ $=$ $180$ $180$ $- 60$ $-60$ Subtract $60$ $60$ from both sides

$y$ $y$ $=$ $=$ $120 °$ $120°$

Finally, add the value of $x$ $x$ and $y$ $y$ to get the value of $k$ $k$

$k$ $k$ $=$ $=$ $x$ $x$ $+$ $+$ $y$ $y$

$k$ $k$ $=$ $=$ $130$ $130$ $+$ $+$ $120$ $120$ Plug in the known values

$k$ $k$ $=$ $=$ $250 °$ $250°$

$∠ k = 250 °$ $/_ k=250°$

$∠ D C E + 45$ $/_DCE+45$	$=$ $=$	$180$ $180$
$∠ D C E + 45$ $/_DCE+45$ $- 45$ $-45$	$=$ $=$	$180$ $180$ $- 45$ $-45$	Subtract $45$ $45$ from both sides
$∠ D C E$ $/_DCE$	$=$ $=$	$135 °$ $135°$

$∠ D C B + 55$ $/_DCB+55$	$=$ $=$	$180$ $180$
$∠ D C B + 55$ $/_DCB+55$ $- 55$ $-55$	$=$ $=$	$180$ $180$ $- 55$ $-55$	Subtract $55$ $55$ from both sides
$∠ D C B$ $/_DCB$	$=$ $=$	$125 °$ $125°$

$a +$ $a+$ $∠ D C E$ $/_DCE$ $+$ $+$ $∠ D C B$ $/_DCB$	$=$ $=$	$360$ $360$
$a + 135 + 125$ $a+135+125$	$=$ $=$	$360$ $360$	Plug in the known values
$a + 260$ $a+260$	$=$ $=$	$360$ $360$	Simplify
$a + 260$ $a+260$ $- 260$ $-260$	$=$ $=$	$360$ $360$ $- 260$ $-260$	Subtract $260$ $260$ from both sides
$a$ $a$	$=$ $=$	$100 °$ $100°$

Angles and Parallel Lines

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Quiz summary

Information

1. Question

Hint

Correct!

Vertically Opposite Angles

Corresponding Angles

Co-Interior Angles

2. Question

Hint

Fantastic!

Alternate Angles

Corresponding Angles

Co-Interior Angles

3. Question

Hint

Keep Going!

Alternate Angles

Corresponding Angles

Co-Interior Angles

4. Question

Hint

Excellent!

Alternate Angles

Corresponding Angles

Co-Interior Angles

Quizzes

$∠ A C D + 122$ $/_ACD+122$	$=$ $=$	$180$ $180$
$∠ A C D + 122$ $/_ACD+122$ $- 122$ $-122$	$=$ $=$	$180$ $180$ $- 122$ $-122$	Subtract $122$ $122$ from both sides
$∠ A C D$ $/_ACD$	$=$ $=$	$58 °$ $58°$

$∠ B D C + 95$ $/_BDC+95$	$=$ $=$	$180$ $180$
$∠ B D C + 95$ $/_BDC+95$ $- 95$ $-95$	$=$ $=$	$180$ $180$ $- 95$ $-95$	Subtract $95$ $95$ from both sides
$∠ B D C$ $/_BDC$	$=$ $=$	$85 °$ $85°$

$x$ $x$ $+ 50$ $+50$	$=$ $=$	$180$ $180$
$x$ $x$ $+ 50$ $+50$ $- 50$ $-50$	$=$ $=$	$180$ $180$ $- 50$ $-50$	Subtract $60$ $60$ from both sides
$x$ $x$	$=$ $=$	$130 °$ $130°$

$y$ $y$ $+ 60$ $+60$	$=$ $=$	$180$ $180$
$y$ $y$ $+ 60$ $+60$ $- 60$ $-60$	$=$ $=$	$180$ $180$ $- 60$ $-60$	Subtract $60$ $60$ from both sides
$y$ $y$	$=$ $=$	$120 °$ $120°$

$k$ $k$	$=$ $=$	$x$ $x$ $+$ $+$ $y$ $y$
$k$ $k$	$=$ $=$	$130$ $130$ $+$ $+$ $120$ $120$	Plug in the known values
$k$ $k$	$=$ $=$	$250 °$ $250°$