Question

Which types of quadrilateral have exactly three right angles?

Answer 1

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.

Answer 2

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!