carolinemurto
Answered



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°

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. class=

Verified Answer :

caylus

Hello,

Arc CD=180°-48°=132°

the measure of ∠DBC=132°/2 =66°

Answer B

TaeKwonDoIsDead

Answer:

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 \(0.5x\) ]


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°.

View image TaeKwonDoIsDead

Related Questions