Two angles of a hexagon are 120° and 160°. If the remaining four angles are equal, find each equal angle.

According to the properties of polygons, if a polygon has n sides, then the sum of its interior angles is (2n - 4) x 90°.

A hexagon have 6 sides.

So, the sum of its interior angles is:

(2 x 6 - 4) x 90°

= (12 - 4) x 90°

= 8 x 90°

= 720°

It is given that two angles of the hexagon are 120° and 160°, and the remaining four angles are equal.

Let each of the equal angles be x°.

So,

120° + 160° + x° + x° + x° + x° = 720°

⇒ 280° + 4x° = 720°

⇒ 4x° = 720° - 280°

⇒ 4x° = 440°

⇒ x° = $\dfrac{440°}{4}$

⇒ x° = 110°

Hence, the measure of each of the four equal angles in the hexagon is 110°.