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23 Sep 2021, 02:00
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C
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Difficulty:
65%
(hard)
Question Stats:
56% (02:52) correct
44%
(02:42)
wrong
based on 39
sessions
History
Date
Time
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Not Attempted Yet
ABCDE is a regular pentagon with a point O inside it, such that OCD is an equilateral triangle. What is the measure of angle AEO (in degrees)?
A. 30
B. 40
C. 42
D. 45
E. 50
A. 30
B. 40
C. 42
D. 45
E. 50
23 Sep 2021, 08:12
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Bunuel
Observe the graph below. We have a couple of things we need to identify:
(1) A pentagon has 360 + 180 = 540 total degrees, and each angle is 540/5 = 108 degrees.
(1) AO bisects angle EAB.
(2) OC = OD = DE. So triangle ODE is an isosceles triangle.
\(\angle DOA = (360 - 60)/2 = 150\)
\(\angle EAO = 108/2 = 54\)
\(\angle OED = (180 - 48)/2 = 66\).
Using quadrilateral AEDO, we can find \(\angle AEO = 360 - 54 - 150 - 48 - 66 = 42\)
Ans: C
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