Answer
Statements
1. $\overline{MN} \parallel \overline{OP}$ in Circle $O$
2. $\angle{1} \cong \angle{2}$
3. $m\angle{1} = m\angle{2}$
4. $m\angle{1} = \frac{1}{2}(m\overparen{MQ})$
5. $m\angle{2} = m\overparen{NP}$
6. $\frac{1}{2}(m\overparen{MQ}) = m\overparen{NP}$
7. $m\overparen{MQ} = 2(m\overparen{NP})$
Work Step by Step
Reasons
1. Given
2. If lines are $\parallel$ then alternate interior angles are congruent
3. Congruent angles have equal measures
4. Measure of inscribed $\angle$ = $\frac{1}{2}$ of intercepted arc
5. Measure of central $\angle$ = Measure of intercepted arc
6. Substitution
7. Multiplication Property of Equality