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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum

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

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Difficulty:   45% (medium)

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

HideShow timer Statistics  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 [ 19.89 KiB | Viewed 381 times ]

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GMAT 1: 550 Q46 V20 Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum  [#permalink]

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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.

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

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Bunuel wrote: 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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IMO E

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

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Math Expert V
Joined: 02 Aug 2009
Posts: 7765
Re: Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum  [#permalink]

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1
1
Archit3110 wrote:
Bunuel wrote: 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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Joined: 18 Aug 2017
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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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chetan2u

thank you

chetan2u wrote:
Archit3110 wrote:
Bunuel wrote: 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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If you liked my solution then please give Kudos. Kudos encourage active discussions. 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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