Question

Find x and y and explain your answer

Answer 1

x = 30

y = 59.33

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=(90)/(3) = 30`

Also

`\angle B + \angle D =180\°\\\\2y-3+y+5=180\\\\3y+2=180\\\\3y=180-2\\\\3y=178\\\\y=(178)/(3) =59.33`

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