Question

quadrilaterals test review sheet

1. find $am$ in the parallelogram if $pn = 15$ and $ao = 5$. the diagram is not to scale.

a. 10
b. 5
c. 15
d. 7.5

1. $lmno$ is a parallelogram. if $nm = x + 24$ and $ol = 5x + 8$, find the value of $x$ and then find $nm$ and $ol$.

a. $x = 6, nm = 30, ol = 30$
b. $x = 4, nm = 30, ol = 28$
c. $x = 6, nm = 28, ol = 30$
d. $x = 4, nm = 28, ol = 28$

1. if $m\angle b = m\angle d = 46$, find $m\angle c$ so that quadrilateral $abcd$ is a parallelogram. the diagram is not to scale.

a. 134
b. 92
c. 46
d. 268

1. find values of $x$ and $y$ for which $abcd$ must be a parallelogram. the diagram is not to scale.

a.
b.
c.
d. $x = 2, y = 5$

Explanation:

Problem 1

Step1: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $AM = AO$.

Step2: Substitute given value

Given $AO = 5$, so $AM = 5$.

Step1: Use parallelogram side property

In a parallelogram, opposite sides are equal, so $NM = OL$.

Step2: Set up equation

$x + 24 = 5x + 8$

Step3: Solve for x

$24 - 8 = 5x - x$
$16 = 4x$
$x = \frac{16}{4} = 4$

Step4: Calculate NM and OL

$NM = 4 + 24 = 28$, $OL = 5(4) + 8 = 28$

Step1: Use parallelogram angle property

In a parallelogram, consecutive angles are supplementary, so $m\angle B + m\angle C = 180^\circ$.

Step2: Solve for $m\angle C$

$m\angle C = 180^\circ - m\angle B$

Step3: Substitute given value

Given $m\angle B = 46^\circ$, so $m\angle C = 180^\circ - 46^\circ = 134^\circ$

Answer:

B. 5

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Problem 2