The value for x and y are 140° and 70° respectively.
How to solve Polygon Question
There are two ways to solve polygon question. Formula for the sum of interior angle and sum of the exterior angle of regular polygon.
Sum of the interior = (n - 2)180
Sum of the exterior = 360/n
Where n = number of sides of a polygon.
The regular polygon in which x is one of its angle is called decagon
Sum of the interior = (n - 2)180
n = 10
Substitute n into the formula
Sum of the interior angle = (10 - 2)180
Sum of the interior angle = (8)180
Sum of the interior angle = 1440
Each angle = 1400/10
x = 140°
For y, the three angles are similar.
sum of angle in a triangle = 180
Since the each triangle is an isoceles triangle, angle at each base will be y
40 + y + y = 180
2y = 180 - 40
2y = 140
y = 70°
Therefore, the value for x and y are 140° and 70° respectively.
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