The value of angle O at the center of the intersecting chords is 56⁰ (Option C).
How to calculate the value of m < O?
The value of angle m <0 is calculated by applying the following circle theorem for angle subtended at the circumference of a circle.
This theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.
The value of arc QN is calculated as;
arc QN = 2 x ∠R (circumference angle of intersecting chords)
arc QN = 2 (28⁰)
arc QN = 56⁰
The value of angle O is calculated as follows;
m ∠ O = arc QN (center angle of intersecting chords)
m ∠ O = 56⁰