Question

in the figure below, point o is the center of the circle and ( mwidehat{rq} = 35^circ ).
what is ( mangle poq )?
( 125^circ )
( 145^circ )
( 135^circ )
( 70^circ )

Explanation:

Step1: Identify the straight line

Since \( PR \) is a diameter of the circle (passes through center \( O \)), \( \angle POR = 180^\circ \) (a straight angle).

Step2: Use the given arc measure

We know \( m\overarc{RQ}=35^\circ \), and the central angle \( \angle ROQ \) is equal to the measure of arc \( RQ \), so \( m\angle ROQ = 35^\circ \).

Step3: Calculate \( m\angle POQ \)

To find \( m\angle POQ \), we subtract \( m\angle ROQ \) from \( m\angle POR \):
\( m\angle POQ = m\angle POR - m\angle ROQ = 180^\circ - 35^\circ = 145^\circ \).

Answer:

\( 145^\circ \) (corresponding to the option with \( 145^\circ \))