Question

In the diagram, AB, BC and CD are three sides of a regular polygon P. a) Work out the size of angle y. square polygon P B C D square regular 12-sided polygon b) Work out the size of angle z. c) What is the name of polygon P? (2) (1) (1) Total marks: 4​

Answer 1

a. The size of the interior angle y for the polygon P is equal to 150°

b. The size of the angle Z is 120°

c. The name of the polygon is dodecagon

How to calculate for the angles using interior angle of the polygon P.

To calculate the sum of interior angles of a polygon, you can use the following formula:

Sum of interior angles = (n - 2) x 180 degrees

Where "n" represents the number of sides (or vertices) of the polygon.

a. Given the 12 sided polygon;

(12 - 2) × 180 = 1800

y {one interior angle} = 1800/12 = 150°

b. z + 90° + 150° = 360° {sum of angles at a point}

z + 240 = 360

z = 360 - 240

z = 120°

c. A regular polygon with twelve sides is called a dodecagon.

Therefore, the size of the interior angle y for the dodecagon is equal to 150° and the size of the angle Z is 120°.