Quadrilateral Geometry 1

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Geometry

Angles

Quadrilateral Geometry

Quadrilateral Geometry 1

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Question 1 of 5

1. Question
Find the value of $h$
- $h=$ (58) $°$
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The sum of the interior angles in a quadrilateral is $360°$

Since the interior angles of a quadrilateral add to $360°,$ add the angle measures and set their sum to $360°.$ Then, solve for $h$ .

$h+78+126+98$ $=$ $360$

$h+302$ $=$ $360$ Simplify

$h+302$ $-302$ $=$ $360$ $-302$ Subtract $302$ from both sides

$h$ $=$ $58°$

$/_ h=58°$
Question 2 of 5

2. Question
Find the value of $x$
- $x=$ (116) $°$
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The sum of the interior angles in a quadrilateral is $360°$

Since the interior angles of a quadrilateral add to $360°,$ add the angle measures and set their sum to $360°.$ Then, solve for $x$ .

$x+116+64+64$ $=$ $360$

$x+244$ $=$ $360$ Simplify

$x+244$ $-244$ $=$ $360$ $-244$ Subtract $244$ from both sides

$x$ $=$ $116°$

$/_ x=116°$
Question 3 of 5

3. Question
Find the value of $x$
- $x=$ (92) $°$
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The sum of the interior angles in a quadrilateral is $360°$

Since the interior angles of a quadrilateral add to $360°,$ add the angle measures and set their sum to $360°.$ Then, solve for $x$ .

Note that the angle marked with a square is a right angle, which is equal to $90°.$

$x+90+86+92$ $=$ $360$

$x+268$ $=$ $360$ Simplify

$x+268$ $-268$ $=$ $360$ $-268$ Subtract $268$ from both sides

$x$ $=$ $92°$

$/_ x=92°$

Question 4 of 5

Find the value of

$x$

$x=$ (6)

Question 5 of 5

5. Question
Find the value of $a$
- $a=$ (97) $°$
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The sum of the interior angles in a quadrilateral is $360°$

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

Find the missing interior angle, then solve for its supplementary angle.

Since the interior angles of a quadrilateral add to $360°,$ add the angle measures and set their sum to $360°.$ Then, solve for the missing angle.

$x+112+81+84$ $=$ $360$ Let $x$ be the missing angle

$x+277$ $=$ $360$ Simplify

$x+277$ $-277$ $=$ $360$ $-277$ Subtract $277$ from both sides

$x$ $=$ $83°$

Next, we can see from the diagram that the exterior angle $a$ and the interior angle $x$ lie on a straight line. Therefore, they are supplementary angles

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

$a+83$ $=$ $180$

$a+83$ $-83$ $=$ $180$ $-83$ Subtract $83$ from both sides

$a$ $=$ $97°$

$/_ a=97°$

$12x+3+76+104+105$	$=$	$360$
$12x+288$	$=$	$360$	Simplify
$12x+288$ $-288$	$=$	$360$ $-288$	Subtract $288$ from both sides
$12x$	$=$	$72$
$12x$ $divide12$	$=$	$72$ $divide12$	Divide both sides by $12$
$x$	$=$	$6$

Quadrilateral Geometry 1

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1. Question

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2. Question

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3. Question

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4. Question

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5. Question

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Quizzes

$h+78+126+98$	$=$	$360$
$h+302$	$=$	$360$	Simplify
$h+302$ $-302$	$=$	$360$ $-302$	Subtract $302$ from both sides
$h$	$=$	$58°$

$x+116+64+64$	$=$	$360$
$x+244$	$=$	$360$	Simplify
$x+244$ $-244$	$=$	$360$ $-244$	Subtract $244$ from both sides
$x$	$=$	$116°$

$x+90+86+92$	$=$	$360$
$x+268$	$=$	$360$	Simplify
$x+268$ $-268$	$=$	$360$ $-268$	Subtract $268$ from both sides
$x$	$=$	$92°$

$x+112+81+84$	$=$	$360$	Let $x$ be the missing angle
$x+277$	$=$	$360$	Simplify
$x+277$ $-277$	$=$	$360$ $-277$	Subtract $277$ from both sides
$x$	$=$	$83°$

$a+83$	$=$	$180$
$a+83$ $-83$	$=$	$180$ $-83$	Subtract $83$ from both sides
$a$	$=$	$97°$