Question

A regular polygon is shown below.

Answer 1

Answer:

x + y = 112.5°

Step-by-step 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°

$\Rightarrow x=\frac{360^{\circ}}{8}=45^{\circ}$

Step 2: To find y:

One interior angle of a regular polygon = $\frac{(n-2) \times 180^{\circ}}{n}$

$\frac{(8-2) \times 180^{\circ}}{8}=\frac{6 \times 180^{\circ}}{8}=135^{\circ}$

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

$y=\frac{135^{\circ}}{2}$

Step 3: Add x+ y

$x+y=45^{\circ}+\frac{135^{\circ}}{2}$

x + y = 112.5°