The value of x is 132 and y is 198.
Step-by-step explanation:
The measure of the entire angle in a rotation is 360°.
To find the angle x :
It is given that one part of 360° is 108°
The part of angle inside the regular hexagon can be calculated as (180(n-2))/n
where, n is the number of sides in a regular hexagon. (n=6)
⇒ 180×(6-2) / 6
⇒ 180×4 / 6
⇒ 720 / 6
⇒ 120
Therefore, the interior angle of the regular hexagon = 120°
⇒ x+108+120 = 360
⇒ x = 360 - 228
⇒ x = 132
To find the angle y :
It is given that one part of 360° is 42°
The other part is the interior angle of regular hexagon = 120°
⇒ y+42+120 = 360
⇒ y = 360 - 162
⇒ y = 198
