Angle subtended by a chord on the major arc of a circle is 65 degree. What is the angle subtended by the same chord on the centre of this circle ?

130 degree

Let O, R and PQ be center, a point on the major arc and the aforementioned chord respectively.

So, the major arc for the PQ chord is PRQ.

Hence, \(\angle\)PRQ = \({65}^\circ\)

\(\angle\)POQ is the angle subtended by the same chord, PQ on the center of the circle.

According to the concept,

\(\angle\)POQ = 2 x \(\angle\)PRQ

= \(\angle\)POQ = 2 x \({65}^\circ\)

= \(\angle\)POQ = \({130}^\circ\)

Therefore, the angle subtended by the same chord on the center of the circle is \({130}^\circ\).