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:
[tex]\angle G = \angle Y = 51.43 ^{\circ}[/tex]
[tex]\angle D = \angle R = 128.57 ^{\circ}[/tex]
Step-by-step explanation:
Given
Shape: Parallelogram DGRY
Dimension: [tex]\angle D = \frac{5}{2}\angle Y[/tex]
Required
Find the measure of each angle
D and R are opposite sides & G and Y are also opposite sides.
So, we have:
[tex]\angle D = \angle R = \frac{5}{2}\angle Y[/tex]
and
[tex]\angle G = \angle Y[/tex]
The sum of angles is given as:
[tex]\angle D + \angle G + \angle R + \angle Y=360^{\circ}[/tex]
Substitute values for [tex]\angle D, \angle G \ \& \angle R[/tex]
[tex]\frac{5}{2}\angle Y + \frac{5}{2}\angle Y + \angle Y + \angle Y = 360^{\circ}[/tex]
Take LCM
[tex]\frac{5\angle Y + 5\angle Y + 2\angle Y+ 2\angle Y}{2}= 360^{\circ}[/tex]
[tex]\frac{14\angle Y}{2}= 360^{\circ}[/tex]
Multiply both sides by [tex]\frac{2}{14}[/tex]
[tex]\frac{2}{14} * \frac{14\angle Y}{2}= 360^{\circ} * \frac{2}{14}[/tex]
[tex]\angle Y= 360^{\circ} * \frac{2}{14}[/tex]
[tex]\angle Y= \frac{ 360^{\circ} *2}{14}[/tex]
[tex]\angle Y= \frac{720^{\circ}}{14}[/tex]
[tex]\angle Y= 51.43 ^{\circ}[/tex]
So:
[tex]\angle G = \angle Y = 51.43 ^{\circ}[/tex]
[tex]\angle D = \frac{5}{2}\angle Y[/tex]
[tex]\angle D = \frac{5}{2} * 51.43^{\circ}[/tex]
[tex]\angle D = \frac{5* 51.43^{\circ}}{2}[/tex]
[tex]\angle D = \frac{257.15^{\circ}}{2}[/tex]
[tex]\angle D = 128.57 ^{\circ}[/tex]
Hence:
[tex]\angle D = \angle R = 128.57 ^{\circ}[/tex]
