Alternate, Corresponding and Co-Interior Angles 3

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Question 1 of 5

1. Question
Find the value of $x$ $x$ and $y$ $y$
- $x =$ $x=$ (99) $°$ $°$
  
  $y =$ $y=$ (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 $180 ° .$ $180°.$ Typically, these angles lie on a straight line.

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

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

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

Therefore, $∠ y =$ $/_ y=$ $81 °$ $81°$

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

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

$x + 81$ $x+81$ $=$ $=$ $180$ $180$

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

$x$ $x$ $=$ $=$ $99 °$ $99°$

$∠ x = 99 °$ $/_ x=99°$

$∠ y = 81 °$ $/_ y=81°$
Question 2 of 5

2. Question
Find the value of $a$ $a$
- $a =$ $a=$ (39) $°$ $°$
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Alternate Angles

Corresponding Angles

Co-Interior Angles

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

To solve for $a$ $a$ , add it to $141 °$ $141°$ and set their sum to $180 °$ $180°$ .

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

$a + 141$ $a+141$ $=$ $=$ $180$ $180$

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

$a$ $a$ $=$ $=$ $39 °$ $39°$

$∠ a = 39 °$ $/_ a=39°$
Question 3 of 5

3. Question
Find the value of $x$ $x$
- $x =$ $x=$ (84) $°$ $°$
Correct

Excellent!

Incorrect

Alternate Angles

Corresponding Angles

Co-Interior Angles

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

To solve for $x$ $x$ , add it to $96 °$ $96°$ and set their sum to $180 °$ $180°$ .

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

$x + 96$ $x+96$ $=$ $=$ $180$ $180$

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

$x$ $x$ $=$ $=$ $84 °$ $84°$

$∠ x = 84 °$ $/_ x=84°$
Question 4 of 5

4. Question
Find the value of $x$ $x$
- $x =$ $x=$ (82) $°$ $°$
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Well Done!

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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 $x$ $x$ , add it to $98 °$ $98°$ and set their sum to $180 °$ $180°$ .

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

$x + 98$ $x+98$ $=$ $=$ $180$ $180$

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

$x$ $x$ $=$ $=$ $82 °$ $82°$

$∠ x = 82 °$ $/_ x=82°$

Question 5 of 5

Find the value of

b

$b$

$b =$ $b=$ (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

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

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

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

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

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