Answer:
A) a = 108°
B) b = 24°
Explanation:
A) The formula used to calculate the interior angle of any polygon is;
θ = 180(n - 2)/n
where;
n is the number of sides that the regular polygon has
θ is the interior angle
This polygon with angle a has 5 sides.
Thus;
a = 180(5 - 2)/5
a = 108°
B) Looking at the image again, we have 2 equilateral triangles and 1 isosceles triangle.
So the point of the ap ex of the unshaded triangle, the angle at that point is 360°
All angles in an equilateral triangle is 60°. Thus, ap ex angle of isosceles triangle is;
360 - (108 + 60 + 60)
360 - 228 = 132°
Now, the other two angles of the unshaded isosceles triangle are equal.
Thus;
2b + 132 = 180 (sum of angles in a triangle)
2b = 180 - 132
2b = 48
b = 48/2
b = 24°