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DENIUS [597]
2 years ago
5

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

Mathematics
1 answer:
weqwewe [10]2 years ago
8 0

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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