|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
22 Mar 2021, 03:15
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (01:55) correct
40%
(01:59)
wrong
based on 60
sessions
History
Date
Time
Result
Not Attempted Yet
Quadrilateral ABCD is inscribed in a circle as shown above. What is the measure of angle BCD ?
(A) 110°
(B) 105°
(C) 100°
(D) 95°
(E) 90°
Attachment:
2021-03-09_19-36-29.png [ 21.37 KiB | Viewed 6532 times ]
31 Mar 2021, 15:36
Kudos
Bookmarks
Attachment:
2021-03-09_19-36-29.png [ 24.65 KiB | Viewed 6073 times ]
Two angles at the circumference subtended by the same arc are equal.
Hence,
Angle CAB= Angle CDB = 25
Angle CBD= Angle CAD = 50
Angle ABD= Angle ACD = x
Angle ADB= Angle ACB = y
(50+25)+(y+25)+(x+y)+(50+x)=360
2(x+y)=210
x+y=105
31 Mar 2021, 19:51
Kudos
Bookmarks
Question is trying to trick you into thinking it’s an inscribed rectangle. Obviously that would be too easy.
2 rules covered:
(1) the degree measure of an Arc on the circumference of the circle is measured by the Central angle that “creates” the Arc
(2) and the Central Angle = (2) * (Inscribed angle made that is subtended by the Same Arc)
The degree measure of the entire Arc that is the Circle is 360 deg.
Minor Arc CB ——— Created by Inscribed Angle CAB which = 25 degrees ——-> Central Angle is (2)(25) = 50 deg ———> Arc CB = 50 deg
Minor Arc DC ———-> created by inscribed angle CBD which = 50 deg. ————> central angle subtended by same Arc DC is (2)(50) = 100 deg ———-> Minor Arc DC = 100 deg
The remaining Arc DAB will be:
360 - (minor arc DC) - (minor arc CB) =
360 - (100) - (50) = 210 deg
Major Arc DAB is created by Inscribed Angle DCB, which is the angle we need to find
Inscribed Angle DCB = (1/2) * (210 degree central angle that measures Arc DAB)
Angle DCB = 105 deg
Posted from my mobile device
2 rules covered:
(1) the degree measure of an Arc on the circumference of the circle is measured by the Central angle that “creates” the Arc
(2) and the Central Angle = (2) * (Inscribed angle made that is subtended by the Same Arc)
The degree measure of the entire Arc that is the Circle is 360 deg.
Minor Arc CB ——— Created by Inscribed Angle CAB which = 25 degrees ——-> Central Angle is (2)(25) = 50 deg ———> Arc CB = 50 deg
Minor Arc DC ———-> created by inscribed angle CBD which = 50 deg. ————> central angle subtended by same Arc DC is (2)(50) = 100 deg ———-> Minor Arc DC = 100 deg
The remaining Arc DAB will be:
360 - (minor arc DC) - (minor arc CB) =
360 - (100) - (50) = 210 deg
Major Arc DAB is created by Inscribed Angle DCB, which is the angle we need to find
Inscribed Angle DCB = (1/2) * (210 degree central angle that measures Arc DAB)
Angle DCB = 105 deg
Posted from my mobile device
