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505-555 (Easy)|   Geometry|      
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Bunuel
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In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is 02 Mar 2015, 08:30
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C
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84% (01:46) correct 16% (02:03) wrong based on 202 sessions

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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°

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C
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In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is 02 Mar 2015, 09:04
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sum of all angles = 360
so 60+c+2c+c+40=360
we get c = 65
b= c+40=105 answer is C
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In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is 02 Mar 2015, 19:12
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Bunuel
Attachment:
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°

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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
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In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is 02 Mar 2015, 22:18
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Answer = C = 105

Refer diagram below:

Attachment:
polygons_img5.png
polygons_img5.png [ 10.73 KiB | Viewed 8081 times ]

Let ∠B = x

All other angles come up as shown above

60 + x + x - 40 + 2(x-40) = 360

x = 105
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In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is 08 Mar 2015, 14:07
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Bunuel
Attachment:
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°

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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
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In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is 08 Mar 2015, 22:27
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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:
Show Spoiler
C

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In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is 26 Oct 2016, 11:31
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60+c+40+c+2c = 360

4c = 260 --> c = 65

B = 40+65 = 105

Thus, answer is C
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In the figure above, in irregular quadrilateral ABCD, ∠A = 60°, ∠D is 07 Dec 2022, 04:58
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