Question

Find the value of x. The diagram is not drawn to scale.

Answer 1

C.
`x=99^(\circ)`

Explanation:

We have been given a image. We are asked to find the value of x.

We can see that our given figure is a quadrilateral. We know that all interior angles of a quadrilateral add up-to 360 degrees.

`x^(\circ)+y^(\circ)+125^(\circ)+72^(\circ)=360^(\circ)`

We can see that y and 116 degrees angles are linear angles, so we can set an equation as:

`y^(\circ)+116^(\circ)=180^(\circ)`

`y^(\circ)+116^(\circ)-116^(\circ)=180^(\circ)-116^(\circ)`

`y=64^(\circ)`

Substitute
`y=64^(\circ)` in the equation:

`x^(\circ)+y^(\circ)+125^(\circ)+72^(\circ)=360^(\circ)`

`x^(\circ)+64^(\circ)+125^(\circ)+72^(\circ)=360^(\circ)`

`x^(\circ)+261^(\circ)=360^(\circ)`

`x^(\circ)+261^(\circ)-261^(\circ)=360^(\circ)-261^(\circ)`

`x^(\circ)=99^(\circ)`

`x=99`

Therefore, the value of x is 99.