asked 121k views
0 votes
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. Show your working ​

asked
User Mellort
by
8.3k points

1 Answer

0 votes

Answer:

15°

Explanation:

For consecutive vertices P, Q, R of a regular dodecagon, you want the measure of angle PRQ.

Exterior angle

The exterior angle at any vertex of a regular 12-sided polygon measures ...

360°/12 = 30°

Triangle

The exterior angle just figured is equal to the sum of the base angles of the isosceles triangle PQR. That is, angle R is ...

R = 30°/2 = 15°

The size of angle PQR is 15°.

__

Additional comment

The sum of exterior angles of any convex polygon is 360°. It is often easy to figure the measure of an exterior angle using this relation.

<95141404393>

PQ and QR are 2 sides of a regular 12-sided polygon. PR is a diagonal of the polygon-example-1
answered
User Bratch
by
7.8k points
Welcome to Qamnty — a place to ask, share, and grow together. Join our community and get real answers from real people.