Question

Circle O is shown below. The diagram is not drawn to scale.

Answer 1

Use the result
the angle subtended at the center of a circle by a chord is twice the measure of the angle subtended at any point on the circle (in the same segment) by the same chord.

Answer 2

* same chord or same arc

Answer 3

in the above diagram the chord concerned is RQ

Answer 4

* sorry NQ

Answer 5

I'll gibe you the hints.
Ang. O is a central angle, because it is composed by two radiuses. sg. NO and sg. OQ to be precise.
but in other hand ang. R is a inscribed angle, meaning that it is formed by two chords, sg. RN and sg. RQ.

Now there was a relationship between the arc that it intersects and the measure of the angle.
I will not prove it, because it's very easy to do, so I'll leave that to you, but here's the relationship:
\[<NRQ=\frac{ arc.NQ }{ 2 }\]
so replacing the information:
\[28=\frac{ arc.NQ }{ 2 }\]
now it's just a matter of math and applying the property of a central angle.
I'll leave that part to you.

Answer 6

Thanks!