Question

one diagonal of a rhombus is equal to its side.Find all the angles of the rombhus and find x and y.

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Answer 1

Step-by-step explanation:

In rohumbus PQRS

Diagonal of rohumbus are perpendicular bisector right?

So, in the diagonal PR (taking the intersection as O)

PO = OR

2x-5 = 15

2x = 20

x = 10

SO = OQ

10 = y + 7

y = 10-7

y = 3

Hence x = 10 and y = 3

In Rohumbus TUVW

Angle WTU = UVW [Opposite angles of rohumbus are equal], same goes for angle y

now,

angle ( WTU + TWV + WVU +VUT ) = 360 [angle sum property of Rhombus]

75 + y + 75 + y = 360

2y +150 = 360

2y = 360 - 150

y = 210/2

y = 105

hence y = 105 degrees = Angle TUV.

for angle x

angle TUV + x = 180 [supplementary angles]

y+ x = 180

105 + x = 180

x = 180-105

x = 75 degrees

To be honest your question wasn't exactly clear, so if I wrote the wrong answer or I misunderstood the question please forgive me.

Hope it helps

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