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In the figure above, in irregular quadrilateral \(ABCD,\) \(\angle A = 60^{\circ}, \angle D\) is twice \(\angle C,\) and

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by Vincen » Thu May 07, 2020 11:16 am

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polygons_img5.png
In the figure above, in irregular quadrilateral \(ABCD,\) \(\angle A = 60^{\circ}, \angle D\) is twice \(\angle C,\) and \(\angle B\) is \(40^{\circ}\) more than \(\angle C.\) Find the measure of \(\angle B.\)

A. \(65^{\circ}\)
B. \(85^{\circ}\)
C. \(105^{\circ}\)
D. \(120^{\circ}\)
E. \(135^{\circ}\)

[spoiler]OA=C[/spoiler]

Source: Magoosh
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Re: In the figure above, in irregular quadrilateral \(ABCD,\) \(\angle A = 60^{\circ}, \angle D\) is twice \(\angle C,\)

by Scott@TargetTestPrep » Sat May 09, 2020 12:02 pm
Vincen wrote: ↑
Thu May 07, 2020 11:16 am
 polygons_img5.png

In the figure above, in irregular quadrilateral \(ABCD,\) \(\angle A = 60^{\circ}, \angle D\) is twice \(\angle C,\) and \(\angle B\) is \(40^{\circ}\) more than \(\angle C.\) Find the measure of \(\angle B.\)

A. \(65^{\circ}\)
B. \(85^{\circ}\)
C. \(105^{\circ}\)
D. \(120^{\circ}\)
E. \(135^{\circ}\)

[spoiler]OA=C[/spoiler]

Source: Magoosh
We can let x = the measure of angle C; thus, 2x = the measure of angle D, and x + 40 = the measure of angle B. We can create the equation:

∠A + ∠B + ∠C + ∠D = 360

60 + x + 40 + x + 2x = 360

4x = 260

x = 65

Therefore, the measure of angle B is 65 + 40 = 105 degrees.

Answer: C

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Re: In the figure above, in irregular quadrilateral \(ABCD,\) \(\angle A = 60^{\circ}, \angle D\) is twice \(\angle C,\)

by GMATinsight » Sat May 09, 2020 11:22 pm
Vincen wrote: ↑
Thu May 07, 2020 11:16 am
 polygons_img5.png

In the figure above, in irregular quadrilateral \(ABCD,\) \(\angle A = 60^{\circ}, \angle D\) is twice \(\angle C,\) and \(\angle B\) is \(40^{\circ}\) more than \(\angle C.\) Find the measure of \(\angle B.\)

A. \(65^{\circ}\)
B. \(85^{\circ}\)
C. \(105^{\circ}\)
D. \(120^{\circ}\)
E. \(135^{\circ}\)

[spoiler]OA=C[/spoiler]

Source: Magoosh
Let, C = x
then B = x+40
and D = 2x

Sum of angles in any quadrilateral = 360

A+B+C+D = 360
60+(x+40)+x+2x = 360
i.e. 4x = 260
i.e. x = 65

Now, B = x+40 = 65+40 = 105

Answer: Option C
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