Answer:
x = 30°
Step-by-step explanation:
A polygon is a 2D shape with at least three sides.
Polygons can be regular or irregular. If the angles are all equal, and all the sides are equal length, it is a regular polygon.
Therefore, this shape is an irregular polygon with 4 sides and 4 interior angles.
The formula for calculating the sum of the interior angles of any polygon is: (n - 2) x 180° (where n is the number of sides)
Therefore, for our polygon, the sum of the interior angles is:
(4 - 2) x 180 = 360°
The four angles of this polygon are 50°, x°, x° and the reflex angle (this is the interior angle the "other side" of the 110° angle).
We know that the sum of angles around a point is 360°
Therefore, the reflex angle = 360 - 110 = 250°
So now we can create an equation where we sum all the interior angles and equal them to 360°, then solve for x:
⇒ 50 + x + x + 250 = 360
⇒ 50 + 2x + 250 = 360
⇒ 2x = 360 - 250 - 50
⇒ 2x = 60
⇒ x = 60 ÷ 2
⇒ x = 30°
Reflex angle = an angle greater than 180° and less than 360°
