Question

Two polygons in the diagram below are regular. find angle RQS.

Answer 1

Angle RQS, the outer angle formed by a regular rectangle and a regular hexagon, measures 150 degrees. This is found by subtracting the sum of the rectangle's right angle and hexagon's interior angle from 360 degrees.

To determine the measure of angle RQS, consider the given shapes—a rectangle (RQS) and an adjacent regular hexagon. Since RQS is a rectangle, it contains a right angle measuring 90 degrees. Additionally, a regular hexagon has interior angles of 120 degrees each.

To find the exterior angle RQS, subtract the sum of the rectangle's right angle and the hexagon's interior angle from 360 degrees. Therefore,

`\[ \text{Angle RQS} = 360^\circ - (90^\circ + 120^\circ) = 360^\circ - 210^\circ = 150^\circ. \]`

Hence, angle RQS measures 150 degrees, as it represents the outer angle formed by the rectangle and the regular hexagon.