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3 years ago

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Quadrilateral LMNO has diagonals that intersect at point P. If LP=NP, MP = y + 25, and OP = 5y + 29, find the length of MO such

that LMNO is a parallelogram.. . A.24. B.48. C.61. D.122

2 answers:

salantis [7]3 years ago

8 0

The right answer will be c.61 that is your answer

Zina [86]3 years ago

8 0

Answer:

The correct option is B.

Step-by-step explanation:

Given information: LMNO is a parallelogram, LMNO has diagonals that intersect at point P, LP=NP, MP = y + 25, and OP = 5y + 29.

Diagonals of parallelogram bisects each other.

Since P is the intersection point of diagonal and MO is a diagonal, so

$MP=OP$

$y+25=5y+29$

Subtract y from both the sides.

$y+25-y=5y+29-y$

$25=4y+29$

Subtract 29 from both the sides.

$25-29=4y+29-29$

$-4=4y$

Divide both sides by 4.

$-1=y$

The value of y is -1.

The length of MO is

$MO=MP+OP$

$MO=y+25+5y+29$

$MO=6y+54$

Substitute y=-1 in the above equation.

$MO=6(-1)+54$

$MO=-6+54$

$MO=48$

The length of MO is 48. Therefore the correct option is B.

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The deck that Amos is building is in the shape of a parallelogram, DGRY. The measure of

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Complete Question:

The deck that Amos is building is in the shape of a parallelogram, DGRY. The measure of D is five-halves the measure of Y. Find the measure of each angle of the deck.

Answer:

$\angle G = \angle Y = 51.43 ^{\circ}$

$\angle D = \angle R = 128.57 ^{\circ}$

Step-by-step explanation:

Given

Shape: Parallelogram DGRY

Dimension: $\angle D = \frac{5}{2}\angle Y$

Required

Find the measure of each angle

D and R are opposite sides & G and Y are also opposite sides.

So, we have:

$\angle D = \angle R = \frac{5}{2}\angle Y$

and

$\angle G = \angle Y$

The sum of angles is given as:

$\angle D + \angle G + \angle R + \angle Y=360^{\circ}$

Substitute values for $\angle D, \angle G \ \& \angle R$

$\frac{5}{2}\angle Y + \frac{5}{2}\angle Y + \angle Y + \angle Y = 360^{\circ}$

Take LCM

$\frac{5\angle Y + 5\angle Y + 2\angle Y+ 2\angle Y}{2}= 360^{\circ}$

$\frac{14\angle Y}{2}= 360^{\circ}$

Multiply both sides by $\frac{2}{14}$

$\frac{2}{14} * \frac{14\angle Y}{2}= 360^{\circ} * \frac{2}{14}$

$\angle Y= 360^{\circ} * \frac{2}{14}$

$\angle Y= \frac{ 360^{\circ} *2}{14}$

$\angle Y= \frac{720^{\circ}}{14}$

$\angle Y= 51.43 ^{\circ}$

So:

$\angle G = \angle Y = 51.43 ^{\circ}$

$\angle D = \frac{5}{2}\angle Y$

$\angle D = \frac{5}{2} * 51.43^{\circ}$

$\angle D = \frac{5* 51.43^{\circ}}{2}$

$\angle D = \frac{257.15^{\circ}}{2}$

$\angle D = 128.57 ^{\circ}$

Hence:

$\angle D = \angle R = 128.57 ^{\circ}$

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