Question

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Answer 1

Answer:

The value of the angle PRQ is 15°

Step-by-step explanation:

we know that the sum of measures of all external angles of a polygon is equal to 360°

Given, sides = 12 (since, it a 12 sided polygon)

Hence, measure of each external angle = sum of external angles/no of sides = 360/12 = 30°

we know that the sum of interior and exterior angles is equal to 180°

therefore, angle PQR = 180° - 30° = 150°

since, it a regular 12 sided polygon

therefore, these two given sides are equal

Hence, it is an Isoceles triangle.

therefore, two angles are also equal.

Let the two angles i.e., PRQ and RPQ be x

Therefore, PRQ+RPQ+PQR = 180°

Or, x + x + 150° = 180°

Or, 2x + 150° = 180°

Or, 2x = 180°-150° = 30°

Or, x = 30°/2 = 15°

therefore, value of PRQ = x = 15° (answer).

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