Question

You are given that the angles of a quadrilateral taken in order are `2x^6, 3x^6, 7x^6` and `6x^6`. Can you say which type of quadrilateral it is?

Answer 1

It is a cyclic quadrilateral.

Explanation:

Perhaps questioner means that

the angles of a quadrilateral taken in order (clockwise or anticlockwise) are `2x^@, 3x^@, 7x^@`, and `6x^@`.

As the sums of alternate pair are equal i.e. `2x^@+7x^@=9x^@=3x^@+6x^@`

but as sum of the angles of a quadrilateral is `360^@`

This means that each pair of opposite angles add up to `180^@` each and hence

It is a cyclic quadrilateral.

Note : In case the angles are not taken in clockwise or anticlockwise order, adjacent angles may add up to `180^@` and quadrilateral may be a trapezium.