Answer:
x = 108°
y = 72°
z = 36°
Step-by-step explanation:
Finding unknown angles:
If all sides are equal in a pentagon, then it is a regular pentagon.
n = the number of sides = 5
Sum of all angles in a pentagon = (n -2) * 180
= (5 - 2)* 180
= 3 *180
= 540°
Sum of each angle of regular pentagon = 540 ÷ 5
= 108°
[tex]\sf \boxed{\bf x= 108^\circ}[/tex]
Linear pair: If the non common arm of adjacent angles form a straight line, then the adjacent angles are called linear pair and they add up to 180°
∠DCB + y = 180 ° {Linear pair}
108 + y = 180
y = 180 - 108
[tex]\sf \boxed{\bf y = 72^\circ}[/tex]
Exterior angle property of triangle: The exterior angle equals the sum of opposite interior angles.
In Δ BCF ,
x = y + z
Now, substitute the values of x and y , and we can find the value of z.
108° = 72 + z
108 - 72 = z
[tex]\sf \boxed{\bf z = 36^\circ}[/tex]
