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Can you please help me

Can you please help me-example-1

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Answer:

x = 90°

y = 30°

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°

_____

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°.

User Dan Haywood
by
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