In circle a shown below, segment bd is a diameter and the measure of arc cb is 48°:

points b, c, d lie on circle a. line segment bd is the diameter of circle a. measure of arc cb is 48 degrees.

what is the measure of ∠dbc?

48°
66°
24°
42°

66°

Step-by-step explanation:

See attached picture.

When an angle intercepts an arc, ARC AC, and forms in the center [central angle], the angle has SAME measure as the ARC AC [denoted by x]. When the angle formed is on the opposite side, it has a measure HALF of that ARC AC [denoted ]

If you look at the problem given, ∠DBC is intercepted by ARC DC and falls in the opposite side of the circle, NOT in the CENTER. Hence ∠DBC has a measure that is HALF of ARC DC.

There are 360 degrees in a circle. ARC DB has 2 endpoints that are the diameter of the circle, so ARC DB has a measure of 180 degrees. Also,

ARC DB = ARC DC + ARC CB

ARC DB = ARC DC + 48

180 = ARC DC + 48

ARC DC = 180 - 48 = 132

Since, ∠DBC = 0.5 * ARC DC, we have:

∠DBC = 0.5 * (132)

∠DBC = 66

Our answer is the second choice of 66°.

the infinity sign

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