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

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Math Expert
Joined: 02 Sep 2009
Posts: 55803
Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum  [#permalink]

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10 Jan 2019, 02:39
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Difficulty:

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

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10 Jan 2019, 02:47

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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Updated on: 11 Jan 2019, 02:32
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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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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11 Jan 2019, 01:55
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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Re: Rectangles lie on sides AB, BC, and AC of ΔABC above. What is the sum  [#permalink]

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11 Jan 2019, 02:26
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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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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