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Is quadrilateral MNPQ a rectangle?

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Is quadrilateral MNPQ a rectangle?  [#permalink]

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New post 03 Jul 2014, 04:45
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Is quadrilateral MNPQ a rectangle?

(1) At least two of the four angles are right angles.
(2) At least three of the four angles are right angles.
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New post 03 Jul 2014, 05:09
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Is quadrilateral MNPQ a rectangle?

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Answer: B.
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New post 03 Jul 2014, 05:10
Bunuel wrote:
Is quadrilateral MNPQ a rectangle?

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Answer: B.


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Re: Is quadrilateral MNPQ a rectangle?  [#permalink]

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New post 04 Jul 2014, 00:08
Bunuel wrote:
Is quadrilateral MNPQ a rectangle?

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Answer: B.


Hello Bunuel

I have a doubt here.
If all 4 angles are 90 degrees then it can be a square also.

We dont know whether all 4 sides or only 2 sides opposite sides are equal ?

So should B be the answer ?
Please correct me

Thankyou.
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New post 04 Jul 2014, 02:48
niyantg wrote:
Bunuel wrote:
Is quadrilateral MNPQ a rectangle?

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Answer: B.


Hello Bunuel

I have a doubt here.
If all 4 angles are 90 degrees then it can be a square also.

We dont know whether all 4 sides or only 2 sides opposite sides are equal ?

So should B be the answer ?
Please correct me

Thankyou.


All squares are rectangles so if MNPQ is a square it's a rectangle too.
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Re: Is quadrilateral MNPQ a rectangle?  [#permalink]

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New post 30 May 2017, 07:20
Bunuel What if all the four angles are 90 but opposite sides are not equal?
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New post 30 May 2017, 07:52
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New post 30 May 2017, 22:00
Hi Banuel,
What if I have a square and tilt it clockwise by 45 degrees.. more like a rhombus..
its not rectangle right?
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Re: Is quadrilateral MNPQ a rectangle?  [#permalink]

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New post 30 May 2017, 22:30
sasidharrs wrote:
Hi Banuel,
What if I have a square and tilt it clockwise by 45 degrees.. more like a rhombus..
its not rectangle right?


Hi

If you take a square and tilt it clockwise, it will still remain a square. When you say tilting, I assume you are just rotating that quadrilateral clockwise or anticlockwise.

A rhombus has all sides equal but all angles are not necessarily equal. So if all the angles are not equal to 90 degrees, then it will definitely not be a rectangle.
But it can surely be a rhombus.
As I wrote, a rhombus has all sides equal but all angles might not be equal, though opposite angles are always equal. A rhombus in which all angles are also equal - then becomes a square. So we say that all squares are rhombuses but all rhombuses are not squares.
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Re: Is quadrilateral MNPQ a rectangle?   [#permalink] 30 May 2017, 22:30
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