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26 Nov 2022, 09:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
58% (02:03) correct
42%
(01:31)
wrong
based on 19
sessions
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Date
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Not Attempted Yet
In quadrilateral ABCD, AB=BC=BD and the measure of angle ABC is 60 degrees What is the measure of angle ADC?
A. 110°
B. 120°
C. 130°
D. 140°
E. 150°
Attachment:
2022-11-25_18-41-40.png [ 20.15 KiB | Viewed 3888 times ]
26 Nov 2022, 10:13
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Let's take triangle ABD first, AB=BD isosceles triangle, so angle A=D=x(let's say)
angle ABD = 180-2x
Now, similarly in triangle DBC, BC=BD, so angle D=C=y(let's say)
angle BDC = 180-2y
Given angle ABC = 60.
Also angle ABC = 180-2x+180-2y.
Therefore 180-2x+180-2y=60
x+y=150.
Also, angle ADC from above two triangles is (x+y).
Hence angle ADC=150.
Hence E is the correct choice.
Posted from my mobile device
angle ABD = 180-2x
Now, similarly in triangle DBC, BC=BD, so angle D=C=y(let's say)
angle BDC = 180-2y
Given angle ABC = 60.
Also angle ABC = 180-2x+180-2y.
Therefore 180-2x+180-2y=60
x+y=150.
Also, angle ADC from above two triangles is (x+y).
Hence angle ADC=150.
Hence E is the correct choice.
Posted from my mobile device
