Angles and Parallel Lines

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Question 1 of 4

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

Corresponding Angles

Co-Interior Angles

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

Vertically Opposite Angles are equal.

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

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

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

$/_ACD+122$ $=$ $180$

$/_ACD+122$ $-122$ $=$ $180$ $-122$ Subtract $122$ from both sides

$/_ACD$ $=$ $58°$

Finally, we can see that angle $/_ACD$ is vertically opposite to angle $x$

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

$/_ x=58°$

Question 2 of 4

Find the value of

$a$

$a=$ (100) $°$

Question 3 of 4

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

Corresponding Angles

Co-Interior Angles

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

Alternate Angles are equal.

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

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

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

$/_BDC+95$ $=$ $180$

$/_BDC+95$ $-95$ $=$ $180$ $-95$ Subtract $95$ from both sides

$/_BDC$ $=$ $85°$

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

Therefore, $/_ x=85°$

$/_ x=85°$
Question 4 of 4

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

Corresponding Angles

Co-Interior Angles

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

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

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 $50°$ and $x$ are co-interior angles, which add to $180°$

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

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

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

$x$ $=$ $130°$

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

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

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

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

$y$ $=$ $120°$

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

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

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

$k$ $=$ $250°$

$/_ k=250°$

$/_DCE+45$	$=$	$180$
$/_DCE+45$ $-45$	$=$	$180$ $-45$	Subtract $45$ from both sides
$/_DCE$	$=$	$135°$

$/_DCB+55$	$=$	$180$
$/_DCB+55$ $-55$	$=$	$180$ $-55$	Subtract $55$ from both sides
$/_DCB$	$=$	$125°$

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

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

$/_ACD+122$	$=$	$180$
$/_ACD+122$ $-122$	$=$	$180$ $-122$	Subtract $122$ from both sides
$/_ACD$	$=$	$58°$

$/_BDC+95$	$=$	$180$
$/_BDC+95$ $-95$	$=$	$180$ $-95$	Subtract $95$ from both sides
$/_BDC$	$=$	$85°$

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

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

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