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 s
1 answer:
Answer:
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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