Answer:
∠ N = 10° , arc RS = 134°
Step-by-step explanation:
the measure of an inscribed angle is half the measure of its intercepted arc.
(5)
∠ N is an inscribed angle and we require arc LM
the measure of the arcs in a circle = 360°
note LN is the diameter so arc LN = 180°
Then
LM + MN + LN = 360°
LM + 160° + 180° = 360°
LM + 340° = 360° ( subtract 340° from both sides )
LM = 20°
then
∠ N = [tex]\frac{1}{2}[/tex] LM = [tex]\frac{1}{2}[/tex] × 20° = 10°
(6)
∠ Q is an inscribed angle so its intercepted arc is twice its measure
arc RS = 2 × 67° = 134°
