Question

burtin, jacameron
formative: unit 6: g.gsr.8.1 abridged
4 of 5
if $m\overparen{ab} = 30^\circ$ and $m\overparen{cd} = 110^\circ$, find $m\angle e$.
15°
30°
40°
70°

Explanation:

Step1: Recall external angle theorem

The measure of an angle formed outside a circle by two secants is half the difference of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The intercepted arcs are $\overset{\frown}{CD}$ (110°) and $\overset{\frown}{AB}$ (30°).

Step3: Calculate $m\angle E$

$m\angle E = \frac{1}{2}(m\overset{\frown}{CD} - m\overset{\frown}{AB})$
$m\angle E = \frac{1}{2}(110^\circ - 30^\circ) = \frac{1}{2}(80^\circ)$

Answer:

40°