Question

How do you solve this

Answer 1

Let
`z^\circ` be the measure of the unlabeled arc. Then

`x^\circ+y^\circ+z^\circ=360^\circ`

The arc with measure
`y^\circ` is subtended by a central angle of 180 degrees. We know this because the chord in the picture passes through the circle's center, so it must be the circle's diameter.

So we have

`x^\circ+z^\circ=180^\circ`

By the inscribed angle theorem, the inscribed angle of measure 36 degrees has half the measure of the central angle subtended by the same arc. This means
`z^\circ=2\cdot36^\circ=72^\circ`.

So

`x^\circ=108^\circ`