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# If the sum of the degree measures of two specific angles of triangle T

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
If the sum of the degree measures of two specific angles of triangle T  [#permalink]

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11 Oct 2017, 00:50
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Difficulty:

95% (hard)

Question Stats:

33% (02:08) correct 67% (01:47) wrong based on 101 sessions

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If the sum of the degree measures of two specific angles of triangle T is greater than the sum of the degree measures of two specific angles of quadrilateral Q, what is the greatest possible number of right angles that Q could have?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

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Joined: 02 Aug 2009
Posts: 8023
If the sum of the degree measures of two specific angles of triangle T  [#permalink]

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11 Oct 2017, 06:40
2
Bunuel wrote:
If the sum of the degree measures of two specific angles of triangle T is greater than the sum of the degree measures of two specific angles of quadrilateral Q, what is the greatest possible number of right angles that Q could have?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

Hi...
We are looking for the max number of 90° angles in Quadrilateral..

1) CAN it be 4.... NO
For all 4 to be 90°, sum of two angles will be 90+90=180 and therefore the sum of two angles of triangle will have to be >180...... Not possible
2) Can it be 3.....NO
3 of angles as 90 means 4th also has to be 90..
3) Can it be 2.... YES
Say sum of angles is 92, so sum of two angles of quadrilateral can be 91, 90° and 1°... In the remaining two, one can be 90 and other 180-1=179

Ans C
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Re: If the sum of the degree measures of two specific angles of triangle T  [#permalink]

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12 Feb 2018, 07:16
1
chetan2u wrote:
Bunuel wrote:
If the sum of the degree measures of two specific angles of triangle T is greater than the sum of the degree measures of two specific angles of quadrilateral Q, what is the greatest possible number of right angles that Q could have?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

Hi...
We are looking for the max number of 90° angles in Quadrilateral..

1) CAN it be 4.... NO
For all 4 to be 90°, sum of two angles will be 90+90=180 and therefore the sum of two angles of triangle will have to be >180...... Not possible
2) Can it be 3.....NO
3 of angles as 90 means 4th also has to be 90..
3) Can it be 2.... YES
Say sum of angles is 92, so sum of two angles of quadrilateral can be 91, 90° and 1°... In the remaining two, one can be 90 and other 180-1=79

Ans C

Dear Chetan,

Thank you for the great explanation.

But you may want to change the above highlighted to 179. It initially confused me while skimming as (360 - (90+1+79)) does not 90. Just letting you know.

Regards,
Louis
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Joined: 02 Apr 2014
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Re: If the sum of the degree measures of two specific angles of triangle T  [#permalink]

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01 Mar 2018, 13:24
Definitely can't be 3 or 4, if quadrilateral has 3 90 degrees, automatically 4 angle is 90, so sum of any specific two angle is 180, which can't be less than sum of two specific angles of triangles (as sum of angles = 180)

It can be 2. Please refer to below Kite diagram.
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IMG_20180302_015314.jpg [ 941.66 KiB | Viewed 500 times ]

Re: If the sum of the degree measures of two specific angles of triangle T   [#permalink] 01 Mar 2018, 13:24
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