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In the figure shown, AC = 2 and BD = DC = 1. What is the measure of
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Updated on: 16 Apr 2018, 12:40

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AbdurRakib wrote:

Attachment:

2018.OG.05.026.q.png

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°

If AC = 2 and DC = 1, then we can conclude that AD = 1 Add this information to the diagram...

If AD = 1 and BD = 1, then ∆ABD is an ISOSCELES triangle, which means ∠DAB = ∠ABD are EQUAL...

If we let x = BOTH ∠DAB and ∠ABD, then we can use the fact that angles in a triangle add to 180º We can write: x + x + 120 = 180 Simplify: 2x + 120 = 180 Solve: x = 30

In other words, ∠ABD = 30º

Answer: C

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Originally posted by GMATPrepNow on 03 Jul 2017, 12:14.
Last edited by GMATPrepNow on 16 Apr 2018, 12:40, edited 1 time in total.

Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of
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04 Jul 2017, 02:55

Angle BDC is 60 degree(because the angle in a straight line is equal to 180 degree) Since BD = DC(as given in the question stem) the triangle must be equilateral. Therefere DC=1.

Since AC=2, AD = AC - DC = 1 Angle ABD = Angle DAB = x(Angles opposite equal sides are equal)

We know that the sum of angles in a triangle is 180 degree, 2x + 120 = 180 Angle ABD(x) = 30 degree(Option C) _________________

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Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of
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15 Nov 2017, 16:46

AbdurRakib wrote:

Attachment:

2018.OG.05.026.q.png

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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