Question

A regular polygon is shown below.

What is the sum of the values of x and y?

105.0

112.5

120.0

135.0

Answer 1

x + y = 112.5°

Explanation:

Step 1 : To find x:

Number of sides in a given regular polygon, n = 8

Each of the angles around a point is xº because given is a regular polygon.

Sum of all the angles of around a point is 360°.

⇒ 8x = 360°

`\Rightarrow x=(360^(\circ))/(8)=45^(\circ)`

Step 2: To find y:

One interior angle of a regular polygon =
`((n-2) * 180^(\circ))/(n)`

`((8-2) * 180^(\circ))/(8)=(6 * 180^(\circ))/(8)=135^(\circ)`

In the given figure, each interior angle is divided by a bisector.

`y=(135^(\circ))/(2)`

Step 3: Add x+ y

`x+y=45^(\circ)+(135^(\circ))/(2)`

x + y = 112.5°