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OG2018 PS In the figure shown

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by fmillar » Tue Aug 29, 2017 12:21 am
Hi there, here comes my first reply ! (let me know if I need to post answers differently)

1) Angle BDC = 60 as it is the complement of ADB (120+60=180)
2) BDC=60 then DBC + DCB = 120, but as BD=DC then DBC=DCB=60 (so an equilateral triangle)
3) Now check that AC =2 but DC=1 therefore AD=1 (AC-DC=2-1)
4) AD =1 but also BD =1 then triangle ADB is isosceles
5) If ADB =120 then DAB+ABD=60 (isosceles), as consequence DAB =30 and ABD=30
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by Jay@ManhattanReview » Tue Aug 29, 2017 8:41 pm
lionsshare wrote:Image


In the figure shown, AC = 2 and BD = DC = 1. What is the measure of angle ABD?

A. 15°
B. 20°
C. 30°
D. 40°
E. 45°

OA: C

Please share your solution for this problem.
We have to find out the value /_ABD.

We know that AC = 2 and DC = 1, thus AD = AC - DC = 2 - 1 = 1

Thus, in ∆ABD, AD = BD = 1. Thus, it's an isosceles triangle.

/_ABD + /_BDA + /_DAB = 180

2*/_ABD + /_BDA = 180

/_ABD = (180 - 120)/2 = 30

The correct answer: C

Hope this helps!

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by Scott@TargetTestPrep » Wed Nov 15, 2017 3:49 pm
lionsshare wrote:Image


In the figure shown, AC = 2 and BD = DC = 1. What is the measure of angle ABD?

A. 15°
B. 20°
C. 30°
D. 40°
E. 45°
Since AC = 2 and DC = 1, AD must be 1. Since BD = 1, this makes triangle ABD an isosceles triangle with angle D as the vertex angle and angles A and ABD as the base angles. We know that angles A and ABD are equal because the sides opposite them are equal. If we let each of the base angles = x, we can create the following equation:

x + x + 120 = 180

2x = 60

x = 30

Answer: C

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by [email protected] » Tue Jun 12, 2018 4:12 pm
Hi All,

We're told that in the figure shown, AC = 2 and BD = DC = 1. We're asked for the measure of angle ABD.

To start, we know that the drawing is not to scale, so we cannot use the shapes in the picture to estimate an answer. However, we can use any numbers/variables that appear in the picture.

We know that BD and DC are BOTH equal to 1. Since AC equals 2, we know that AD equals 1 (since 2 - 1 = 1). Thus, triangle ABD is ISOSCELES.

We know one of the angles in triangle ABD (re: 120 degrees) and since that triangle is isosceles, the other two angles MUST be equal and total the missing 60 degrees in that triangle. Thus, those two angles are BOTH 30 degrees.

Final Answer: C

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