Alternate, Corresponding and Co-Interior Angles 3

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Question 1 of 5

1. Question
Find the value of $x$ and $y$
- $x=$ (99) $°$
  
  $y=$ (81) $°$
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Alternate Angles

Corresponding Angles

Co-Interior Angles

Corresponding Angles are equal.

Supplementary angles are when two angles have a sum of $180°.$ Typically, these angles lie on a straight line.

First, notice that $y$ and $81°$ are corresponding angles.

Then, to solve for $x$ , get the supplementary angle of $81°$ .

First, we can see from the diagram that $81°$ and $y$ are corresponding angles, which means they are equal

Therefore, $/_ y=$ $81°$

Notice that $x$ lies on a line that is also parallel to $81°$ and $y$ . This means that the angle supplementary to $x$ also measures $81°$

Finally, since supplementary angles add to $180°,$ add $x$ and $81°$ and set their sum to $180°.$ Then, solve for the value of $x$ .

$x+81$ $=$ $180$

$x+81$ $-81$ $=$ $180$ $-81$ Subtract $81$ from both sides

$x$ $=$ $99°$

$/_ x=99°$

$/_ y=81°$
Question 2 of 5

2. Question
Find the value of $a$
- $a=$ (39) $°$
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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 $a$ , add it to $141°$ and set their sum to $180°$ .

We can see from the diagram that $141°$ and $a$ are co-interior angles, which add up 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 $a$ .

$a+141$ $=$ $180$

$a+141$ $-141$ $=$ $180$ $-141$ Subtract $141$ from both sides

$a$ $=$ $39°$

$/_ a=39°$
Question 3 of 5

3. Question
Find the value of $x$
- $x=$ (84) $°$
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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 $x$ , add it to $96°$ and set their sum to $180°$ .

We can see from the diagram that $96°$ 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 $x$ .

$x+96$ $=$ $180$

$x+96$ $-96$ $=$ $180$ $-96$ Subtract $96$ from both sides

$x$ $=$ $84°$

$/_ x=84°$
Question 4 of 5

4. Question
Find the value of $x$
- $x=$ (82) $°$
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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 $x$ , add it to $98°$ and set their sum to $180°$ .

We can see from the diagram that $98°$ 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 $x$ .

$x+98$ $=$ $180$

$x+98$ $-98$ $=$ $180$ $-98$ Subtract $98$ from both sides

$x$ $=$ $82°$

$/_ x=82°$
Question 5 of 5

5. Question
Find the value of $b$
- $b=$ (48) $°$
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Vertically Opposite Angles

Corresponding Angles

Co-Interior Angles

Vertically Opposite Angles are equal.

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

To solve for $b$ , get the supplementary angle of $132°$ .

First, we can see that angle $132°$ is vertically opposite to angle $a$

Since vertically opposite angles are equal, $/_ a=132°$

Finally, we can see from the diagram that $a$ and $b$ 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 $b$ .

$a+b$ $=$ $180$

$132+b$ $=$ $180$ Plug in the known values

$132+b$ $-132$ $=$ $180$ $-132$ Subtract $132$ from both sides

$b$ $=$ $48°$

$/_ b=48°$

Alternate, Corresponding and Co-Interior Angles 3

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Quiz summary

Information

1. Question

Hint

Great Work!

Alternate Angles

Corresponding Angles

Co-Interior Angles

2. Question

Hint

Keep Going!

Alternate Angles

Corresponding Angles

Co-Interior Angles

3. Question

Excellent!

Alternate Angles

Corresponding Angles

Co-Interior Angles

4. Question

Well Done!

Alternate Angles

Corresponding Angles

Co-Interior Angles

5. Question

Hint

Great Work!

Vertically Opposite Angles

Corresponding Angles

Co-Interior Angles

Quizzes

$x+81$	$=$	$180$
$x+81$ $-81$	$=$	$180$ $-81$	Subtract $81$ from both sides
$x$	$=$	$99°$

$a+141$	$=$	$180$
$a+141$ $-141$	$=$	$180$ $-141$	Subtract $141$ from both sides
$a$	$=$	$39°$

$x+96$	$=$	$180$
$x+96$ $-96$	$=$	$180$ $-96$	Subtract $96$ from both sides
$x$	$=$	$84°$

$x+98$	$=$	$180$
$x+98$ $-98$	$=$	$180$ $-98$	Subtract $98$ from both sides
$x$	$=$	$82°$

$a+b$	$=$	$180$
$132+b$	$=$	$180$	Plug in the known values
$132+b$ $-132$	$=$	$180$ $-132$	Subtract $132$ from both sides
$b$	$=$	$48°$