Robert has made a mask consisting of two triangles and a regular hexagon. Identify all true statements based on the image of Robert’s mask.

Choices:
[]x=72
[]y=162
[]x=120
[]y=138
[]y=198
[]x=132

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

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step-by-step explanation: