Quadrilateral Geometry 2

Question 2 of 4

2. Question
Find the value of $x$ $x$
- $x =$ $x=$ (105) $°$ $°$
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Supplementary angles are when two angles have a sum of $180 ° .$ $180°.$ Typically, these angles lie on a straight line.

Opposite angles of a parallelogram have equal values.

Find the missing supplementary angle, which is equal to the value of $x$ $x$ .

First, we can see from the diagram that the exterior angle $75 °$ $75°$ and the interior angle $∠ A D C$ $/_ADC$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to $180 °,$ $180°,$ add the angle measures and set their sum to $180 ° .$ $180°.$ Then, solve for the value of $a$ $a$ .

$∠ A D C + 75$ $/_ADC+75$ $=$ $=$ $180$ $180$

$∠ A D C + 75$ $/_ADC+75$ $- 75$ $-75$ $=$ $=$ $180$ $180$ $- 75$ $-75$ Subtract $75$ $75$ from both sides

$∠ A D C$ $/_ADC$ $=$ $=$ $105 °$ $105°$

Finally, the angle $∠ A D C$ $/_ADC$ is opposite to angle $x$ $x$

Since opposite angles on a parallelogram are equal, $∠ x = 105 °$ $/_ x=105°$

$∠ x = 105 °$ $/_ x=105°$

Question 3 of 4

Find the value of

a

$a$ ,

b

$b$ , and

c

$c$

$a =$ $a=$ (113) $°$ $°$

$b =$ $b=$ (35) $°$ $°$

$c =$ $c=$ (32) $°$ $°$

Question 4 of 4

Find the value of

∠ B E D

$/_BED$

$∠ B E D =$ $/_BED=$ (57) $°$ $°$

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An Isosceles Triangle has two congruent sides (the two sides with dashes) and the two base angles are equal.

Supplementary angles are when two angles have a sum of

180 ° .

$180°.$ Typically, these angles lie on a straight line.

The sum of the interior angles in a quadrilateral is $360 °$ $360°$

To solve for

∠ B E D

$/_BED$ , first find

∠ E B C

$/_EBC$ . Add these two angles to the two given interior angles, then set their sum to

360 °

$360°$

First, since the base angles in an isosceles triangle are equal, $∠ A B E$ $/_ABE$ is equal to

70 °

$70°$

∠ A B E

$/_ABE$

=

$=$

70 °

$70°$

Next, we can see from the diagram that the angle

∠ A B E

$/_ABE$ and the angle

∠ E B C

$/_EBC$ lie on a straight line. Therefore, they are supplementary angles

Since supplementary angles add to

180 °,

$180°,$ add the angle measures and set their sum to

180 ° .

$180°.$ Then, solve for the value of

∠ E B C

$/_EBC$ .

$∠ E B C + ∠ A B E$ $/_EBC+/_ABE$	$=$ $=$	$180$ $180$
$∠ E B C + 70$ $/_EBC+70$	$=$ $=$	$180$ $180$	Plug in the known values
$∠ E B C + 70$ $/_EBC+70$ $- 70$ $-70$	$=$ $=$	$180$ $180$ $- 70$ $-70$	Subtract $70$ $70$ from both sides
$∠ E B C$ $/_EBC$	$=$ $=$	$110 °$ $110°$

Finally, since the interior angles of a quadrilateral add to

360 °,

$360°,$ add the angle measures and set their sum to

360 ° .

$360°.$ Then, solve for

∠ B E D

$/_BED$ .

$∠ B E D + ∠ E B C + 109 + 84$ $/_BED+/_EBC+109+84$	$=$ $=$	$360$ $360$
$∠ B E D + 110 + 109 + 84$ $/_BED+110+109+84$	$=$ $=$	$360$ $360$	Plug in the known lengths
$∠ B E D + 303$ $/_BED+303$	$=$ $=$	$360$ $360$	Simplify
$∠ B E D + 303$ $/_BED+303$ $- 303$ $-303$	$=$ $=$	$360$ $360$ $- 303$ $-303$	Subtract $303$ $303$ from both sides
$∠ B E D$ $/_BED$	$=$ $=$	$57 °$ $57°$

∠ B E D = 57 °

$/_ BED=57°$

$30 x - 2 + 62 + 62 + 118$ $30x-2+62+62+118$	$=$ $=$	$360$ $360$
$30 x + 240$ $30x+240$	$=$ $=$	$360$ $360$	Simplify
$30 x + 240$ $30x+240$ $- 240$ $-240$	$=$ $=$	$360$ $360$ $- 240$ $-240$	Subtract $240$ $240$ from both sides
$30 x$ $30x$	$=$ $=$	$120$ $120$
$30 x$ $30x$ $\div 30$ $divide30$	$=$ $=$	$120$ $120$ $\div 30$ $divide30$	Divide both sides by $30$ $30$
$x$ $x$	$=$ $=$	$4$ $4$

Quadrilateral Geometry 2

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Quizzes

$∠ A D C + 75$ $/_ADC+75$	$=$ $=$	$180$ $180$
$∠ A D C + 75$ $/_ADC+75$ $- 75$ $-75$	$=$ $=$	$180$ $180$ $- 75$ $-75$	Subtract $75$ $75$ from both sides
$∠ A D C$ $/_ADC$	$=$ $=$	$105 °$ $105°$

$b + c + 113$ $b+c+113$	$=$ $=$	$180$ $180$
$35 + c + 113$ $35+c+113$	$=$ $=$	$180$ $180$	Plug in the known values
$c + 148$ $c+148$	$=$ $=$	$180$ $180$	Simplify
$c + 148$ $c+148$ $- 148$ $-148$	$=$ $=$	$180$ $180$ $- 148$ $-148$	Subtract $148$ $148$ from both sides
$∠ c$ $/_ c$	$=$ $=$	$32 °$ $32°$