ANSWER:
x = 140°
The value of ( x ) is equivalent to 140°. You can find the value of ( x ) by referring to the 'Step-By-Step Explanation' below.
STEP-BY-STEP EXPLANATION:
First, we need to find the value of each internal angle in the regular hexagon PQRSTU. As all the angles in a regular hexagon are equivalent, we will do the following:
Interior angle of a regular shape = Angle sum of shape ÷ No. of interior angles in shape
Interior angle of regular hexagon = Angle sum of regular hexagon ÷ No. of angles in hexagon
Let interior angle of PQRSTU = y
y = 720° ÷ 6
y = 120°
As line PUVW is a straight line:
Angle PUT + Angle VUT = 180°
Angle PUT = y = 120°
THEREFORE:
120° + Angle VUT = 180°
Angle VUT = 180° - 120°
Angle VUT = 60°
As well as this:
Angle STU + Angle UTV + Angle VTS = 360°
Angle STU = y = 120°
Angle VTS = 160°
THEREFORE:
120° + Angle UTV + 160° = 360°
Angle UTV = 360° - 120° - 160°
Angle UTV = 80°
The sum of two interior angles of a triangle which don't share a vertex with an exterior angle of the triangle, is equivalent to the respective exterior angle.
THEREFORE:
Angle WVT = Angle VUT + Angle UTV
x = 60° + 80°
x = 140°
