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slavikrds [6]
3 years ago
7

Find x and y and explain your answer

Mathematics
1 answer:
MrRissso [65]3 years ago
6 0

Answer:

x = <u>30</u>

y = <u>59.33</u>

Step-by-step explanation:

We have Redrawn the diagram by naming the quadrilateral.

Now According to redrawn diagram;

∠ A = 90°

∠ B = (2y-3)\°

∠ C = 3x\°

∠ D = (y+5)\°

We need to find the value of 'x' and 'y'.

Solution:

Now we know that;

"If a quadrilateral whose all four sides or vertices touches the circle then it is said to be cyclic quadrilateral."

The Given diagram is a Cyclic Quadrilateral.

Now By Properties of Cyclic Quadrilateral which states that;

"Sum of the angles of opposite side of quadrilateral is always 180°."

So we can say that;

∠ A + ∠ C = 180°

∠ B + ∠ D = 180°

Substituting the values we get;

\angle A + \angle C = 180\°\\\\90+3x=180\\\\3x=180-90\\\\3x=90\\\\x=\frac{90}{3} = 30

Also

\angle B + \angle D =180\°\\\\2y-3+y+5=180\\\\3y+2=180\\\\3y=180-2\\\\3y=178\\\\y=\frac{178}{3} =59.33

Hence The Value of x is 30 and y is 59.33.

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