Question

In the diagram, AB, BC and CD are three sides of a regular polygon F

A
a) Work out the size of angle y.
square polygon P
B
D
square
regular 12-sided polygon
y z
b) Work out the size of angle z.
c) What is the name of polygon P?

Answer 1

Explanation:

The size of each interior angle of the polygon is 4x+28 °

Answer 2

a) Angle y: 300°

b) Angle z: 510°

c) Polygon P: dodecagon

**a) Size of angle y:**

• Each interior angle of a regular polygon can be calculated using the formula: (180 * (n - 2)) / n where n is the number of sides in the polygon.
• In this case, polygon P has 12 sides, so each interior angle measures: (180 * (12 - 2)) / 12 = 150°
• Angle y is made up of two interior angles of polygon P, so its size is: 2 * 150° = 300°

**b) Size of angle z:**

• Angle z is a reflex angle, which means it is greater than 180°.
• It is made up of four interior angles of polygon P: 4 * 150° = 600°
• However, angle z also includes an acute angle formed by the sides of the two squares.
• This acute angle can be calculated by subtracting the angle between two adjacent sides of a square (90°) from the angle between two opposite sides of a square (180°): 180° - 90° = 90°
• Therefore, the size of angle z is: 600° - 90° = 510°

**c) Name of polygon P:**

• A regular polygon with 12 sides is called a dodecagon.