Question

Tell whether the following set is an empty set or not? A = { A quadrilateral having 3 obtuse angles}

Answer 1

No.

Explanation:

A quadrilateral with 3 obtuse angles is possible. You could have 100°+100°+100°+60° quadrilateral or whatever. As long as it's inner angles add up to 360°, it is possible.

Answer 2

`\boxed{\mathrm{It \: is \: not \: an \: empty \: set}}`

Explanation:

A quadrilateral with 3 obtuse angles is possible.

A obtuse angle has a measure of more than 90 degrees and less than 180 degrees.

Let’s say three angles are measuring 91 degrees in a quadrilateral.

91 + 91 + 91 + x = 360

x = 87

The measure of the fourth angle is 87 degrees which is less than 360 degrees and is a positive integer, so it is possible.