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Answer:
x = 90°
y = 30°
Step-by-step explanation:
The relevant relations are ...
- an inscribed angle is half the measure of the arc it intercepts
- the sum of angles in a triangle is 180°
- the sum of arcs of a circle is 360°
Arc AB is half a circle, so is 180°. Inscribed angle C intercepts that arc, so is half its measure: x = 90°.
The angles of a triangle total 180°, so y has the value that makes the sum of angles be 180°.
y = 180° -90° -60°
y = 30°
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Additional comment
It is worth remembering that a triangle inscribed in a semicircle is a right triangle. This tells you right away that x=90°.
