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Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum

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Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum  [#permalink]

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New post 10 Jan 2019, 02:39
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A
B
C
D
E

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  45% (medium)

Question Stats:

44% (01:23) correct 56% (00:50) wrong based on 34 sessions

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Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum  [#permalink]

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New post 10 Jan 2019, 02:47
My Answer is A 90"

The sum of exterior angles of a triangle is 360-Sum of angles of 3 rectangles ie 270
Would give us resulting measure of 90.

Official answer please!!

Please explain if my answer is incorrect
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Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum  [#permalink]

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New post Updated on: 11 Jan 2019, 02:32
Bunuel wrote:
Image
Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum of the measures of the angles marked?


A. 90°
B. 180°
C. 270°
D. 360°
E. It cannot be determined from the information given


Attachment:
2019-01-10_1338.png


total sum of all three sides ; 360*3 = 1080
and for one side we have two sides of rectangle + 1 angle of triangle +1 external angle
2*90+angle a + ext a
total
3*2*90 + 180+ ext a+ext b+ext c = 1080
ext a+ext b+ext c= 360
IMO D
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Originally posted by Archit3110 on 10 Jan 2019, 06:58.
Last edited by Archit3110 on 11 Jan 2019, 02:32, edited 2 times in total.
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Re: Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum  [#permalink]

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New post 10 Jan 2019, 07:16
IMO E

At first glance, you might finalize 180 but C and D vertices are differently aligned.

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Re: Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum  [#permalink]

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New post 11 Jan 2019, 01:55
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1
Archit3110 wrote:
Bunuel wrote:
Image
Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum of the measures of the angles marked?


A. 90°
B. 180°
C. 270°
D. 360°
E. It cannot be determined from the information given


Attachment:
2019-01-10_1338.png


chetan2u :
Hi could you please review the question and suggest the solution..


Hi..

Each vertice will make 360 when in a complete circle.
Now each vertice consists of two angles of rectangle, one angle at the exterior, say \(E_A\)and one angle of triangle, say A . So 2*90 +A+\(E_A\)

When we add all three vertices for the same .. we have 3*(2*90)+\(E_A+E_B+E_C\)+A+B+C..
We are looking for \(E_A+E_B+E_C\) and A+B+C =180

So 3*(2*90)+\(E_A+E_B+E_C\)+180=3*360...540+180+\(E_A+E_B+E_C\)=1080...
\(E_A+E_B+E_C\)=1080-540-180=360

D
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Re: Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum  [#permalink]

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New post 11 Jan 2019, 02:26
chetan2u

thank you

chetan2u wrote:
Archit3110 wrote:
Bunuel wrote:
Image
Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum of the measures of the angles marked?


A. 90°
B. 180°
C. 270°
D. 360°
E. It cannot be determined from the information given


Attachment:
2019-01-10_1338.png


chetan2u :
Hi could you please review the question and suggest the solution..


Hi..

Each vertice will make 360 when in a complete circle.
Now each vertice consists of two angles of rectangle, one angle at the exterior, say \(E_A\)and one angle of triangle, say A . So 2*90 +A+\(E_A\)

When we add all three vertices for the same .. we have 3*(2*90)+\(E_A+E_B+E_C\)+A+B+C..
We are looking for \(E_A+E_B+E_C\) and A+B+C =180

So 3*(2*90)+\(E_A+E_B+E_C\)+180=3*360...540+180+\(E_A+E_B+E_C\)=1080...
\(E_A+E_B+E_C\)=1080-540-180=360

D

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Re: Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum   [#permalink] 11 Jan 2019, 02:26
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