Question

A kite has angle measures of 7x°, 65°, 85°, and 105°. Find the value of x.

Which of the angles are opposite angles? Explain your reasoning.

Answer 1

Part 1

Angles of a quadrilateral add to 360 degrees.

`7x+65+85+105=360\\\\7x+255=360\\\\7x=105\\\\x=15`

Part 2

If
`x=15`, then
`7x=105^(\circ)`. Thus, the angles measuring
`7x` and
`105^(\circ)` are opposite angles since opposite angles of a kite are congruent.

This means the remaining angles, which are the angles measuring
`65^(\circ)` and
`85^(\circ)`, are also opposite using the process of elimination.