Which types of quadrilateral have exactly three right angles?

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Jan 23, 2016

Quadrilaterals have #4# sides and #4# angles. The exterior angles of any convex polygon (ie no interior angle is less than #180# degrees) add up to #360# degrees (#4# right angles). If an interior angle is a right angle then the corresponding exterior angle must also be a right angle (interior + exterior = a straight line = #2# right angles).

Here #3# internal angles are each right angles, so the corresponding #3# external angles are also right angles, making a total of #3# right angles. The remaining external angle must be #1# right angle #(=4 - 3)#, so the remaining #4th# interior angle is also a right angle.

Therefore, if #3# internal angles are right angles, the 4th angle must also be a right angle.

So no quadrilaterals have exactly #3# right angles.

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[CHAN] Share
May 11, 2017

Answer:

The types of quadrilaterals that have #3# right angles are known as:
- Squares
- Rectangles
- Other shapes where all angles are #90^o#

Explanation:

The reason for this is:

All quadrilaterals interior angles must add up to exactly #360^o#.

So:

= #360 - (90 + 90 + 90)#
= #90#

And thus, the fourth angle must be #90^o#. The only quadrilaterals that fit the description where all angles are #90^o# are squares and rectangles.

All the best!

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