Question

given: in circle i, ( mangle wiq = 140.5^{circ} ) use the interactive diagram to determine ( mwidehat{wq} ) and ( mangle wrq ).

Explanation:

Step1: Find measure of arc WQ

Central angle equals arc measure: $m\overset{\frown}{WQ} = m\angle WIQ = 140.5^\circ$

Step2: Find measure of ∠WRQ

Inscribed angle is half the arc: $m\angle WRQ = \frac{1}{2}m\overset{\frown}{WQ} = \frac{1}{2} \times 140.5^\circ$

Step3: Calculate ∠WRQ

$m\angle WRQ = 70.25^\circ$

Answer:

$m\overset{\frown}{WQ} = 140.5^\circ$, $m\angle WRQ = 70.25^\circ$