PQ and QR are 2 sides of a regular 12-sided polygon. PR is a diagonal of the polygon. Work out the size of angle PRQ. You must show your working.

15°

Step-by-step explanation:

A regular polygon is a polygon in which all the sides and angles of the polygon are equal to each other.

A regular 12-sided polygon is a polygon with 12 equal sides and angles.

The sum of interior angles of a polygon is given as:

sum = (2n - 4)90; where n is the number of sides of the polygon

For a 12 sided polygon:

Sum of interior angles = (2 * 12 - 4)90 = (24 - 4)90 = 20 * 90 = 1800°

Therefore since all the angles are equal, each angle = 1800° / 12 = 150°

Therefore in the question, ∠PQR = 150° (angle of a 12 sided polygon), ∠PRQ = ∠QPR = x

Therefore in triangle PQR:

∠PQR + ∠PRQ + ∠QPR = 180°

150 + x + x = 180

150 + 2x = 180

2x = 30

x = 15°

∠PRQ = 15°

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step-by-step explanation:

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