Answer:
Explanation:
You want the measures of the internal and external angles y° and x° in the figure shown.
Arcs
Let the angle x intercept arcs 'a' and 'b' of the circle, where 'a' is the shorter arc on the left side, and 'b' is the longer arc on the right side.
The measures of the inscribed angles are half the measure of the arcs they intercept:
18° = a/2
34° = b/2
Exterior angle
The angle marked x° is half the difference of the arcs it intercepts:
x° = (b -a)/2 = (b/2) -(a/2) = 34° -18°
x° = 16°
Interior angle
The angle marked y° is half the sum of the arcs in intercepts:
y° = (b +a)/2 = b/2 +a/2 = 34° +18°
y° = 52°
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