In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is

Question

polygons_img5.png In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is twice ∠C, and ∠B is 40° more than ∠C. Find the measure of ∠B A. 65° B. 85° C. 105° D. 120° E. 135° Kudos for a correct solution .

ynaikavde · Answer

sum of all angles = 360
so 60+c+2c+c+40=360 
we get c = 65
b= c+40=105 answer is C

peachfuzz · Answer

Sum of interior angles of a polygon = 180(n-2) where n is the number of sides.

so in this case the sum of the interior angles of this polygon is 360.

from there let angle C = x
360=60+4x+40
x=65
65+40=105

Answer: C

PareshGmat · Answer

Answer = C = 105 Refer diagram below: polygons_img5.png Let ∠B = x All other angles come up as shown above 60 + x + x - 40 + 2(x-40) = 360 x = 105

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

The sum of the four angles in a quadrilateral is 360°. We know ∠A = 60°. Let ∠C = x —- then ∠D = 2x and ∠B = x + 40°.
∠A + ∠B + ∠C + ∠D = 360°
60° + (x + 40°) + x + 2x = 360°
4x + 100° = 360°
4x = 260°
2x = 130°
x = 65° —- that’s the measure of ∠C, and ∠B is 40° more than this.
∠B = 65° + 40° = 105°.

Answer = C

EMPOWERgmatRichC · Answer

Hi All,

In this question, we know one of the angles is 60 and we know that the other 3 angles all relate to Angle C, so setting up an Algebraic solution is a fairly straight-forward way to approach this question. Since the answers are all numbers though, and we're looking for the value of Angle B, we can TEST THE ANSWERS.

First, the facts (what we know and what we're given)
1) The angles of a quadrilateral always total 360 degrees
2) Angle A = 60 degrees
3) Angle D = 2(Angle C)
4) Angle B = Angle C + 40

We're asked for the measure of Angle B.

Since Answer D is the 'nicest' number, let's start there...

IF...
Angle B = 120.....
Angle C = 80
Angle D = 160
The 4 angles total = 60 + 120 + 80 + 160 = 420
This is TOO MANY DEGREES. Angle B MUST be a smaller angle. Eliminate Answers D and E.

IF....
Angle B = 85....
Angle C = 45
Angle D = 90
The 4 angles total = 60 + 85 + 45 + 90 = 280
This is TOO FEW DEGREES. Angle B MUST be a larger angle. Eliminate A and B.

There's only one answer left....

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

law258 · Answer

60+c+40+c+2c = 360

4c = 260 --> c = 65

B = 40+65 = 105

Thus, answer is C

bumpbot · Answer

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In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is

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In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is

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