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°
[tex]\Rightarrow x=\frac{360^{\circ}}{8}=45^{\circ}[/tex]
Step 2: To find y:
One interior angle of a regular polygon = [tex]\frac{(n-2) \times 180^{\circ}}{n}[/tex]
[tex]\frac{(8-2) \times 180^{\circ}}{8}=\frac{6 \times 180^{\circ}}{8}=135^{\circ}[/tex]
In the given figure, each interior angle is divided by a bisector.
[tex]y=\frac{135^{\circ}}{2}[/tex]
Step 3: Add x+ y
[tex]x+y=45^{\circ}+\frac{135^{\circ}}{2}[/tex]
x + y = 112.5°
