Answer:
∠LOP = 96°
Step-by-step explanation:
Given an inscribed angle of 48°, you want to know the measure of the central angle that subtends the same arc.
Inscribed angle
The measure of an inscribed angle is half the measure of the arc it subtends.
∠LMP = 1/2(arc LP)
48° = 1/2(arc LP) . . . . . . use the given value
96° = arc LP . . . . . . . . . multiply by 2
Central angle
The measure of an arc of a circle is the same as the measure of the central angle it subtends: the arc measure and its central angle measure are identical.
arc LP = ∠LOP
96° = ∠LOP
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Additional comment
That's a long way of saying the central angle is twice the inscribed angle that subtends the same arc. ∠LOP = 2×∠LMP.
