In a circle with centre O, PQ and QR are two chords such that ∠ PQR = 118°. What is the measure of ∠ OPR ?

28°

Let P and R meet at point S on the major segment of the circle

Now,

PQRS is a cyclic quadrilateral

So, \(\angle\)PSR + \(\angle\)PQR = \({180}^\circ\)

⇒ \(\angle\)PSR + \({118}^\circ\) = \({180}^\circ\)

⇒ \(\angle\)PSR = \({180}^\circ\) - \({118}^\circ\)

⇒ \(\angle\)PSR = \({62}^\circ\)

Now,

\(\angle\)POR = \({124}^\circ\)

OP = OR = radius of the circle

So, \(\angle\)OPR = (\({180}^\circ\) - \({124}^\circ\))/2

⇒ \(\angle\)OPR = \({56}^\circ\)/2

⇒ \(\angle\)OPR = \({28}^\circ\)

Therefore, \(\angle\)OPR is \({28}^\circ\).