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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

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:

In the figure shown, AC = 2 and BD = DC = 1. What is the measure of
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27 Sep 2019, 08:16

Can someone help me, I have a flaw in my logic. I totally understand it, but I would have solved it from the second triangle.

Is it true that angles in the triangle on the right are 60 degree?

I somehow got stuck because I thought that if those angles are 60, the upper angle (aka the one we are looking for) has to be 120. Is this wrong because it would only be 120 if I would draw a line from up there and the touch on the line would make it 180?

See drawing:

Attachments

aaa.PNG [ 249.06 KiB | Viewed 701 times ]

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