Question

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listen
examine circle o, which has diameter qs.
what are the measures of ∠qts and ∠qus?
use the keypad to enter your answers in the boxes. include the correct symbol for the units of measure.

Explanation:

Step1: Recall Thales' theorem

Thales' theorem states that if you have a triangle inscribed in a circle where one side of the triangle is the diameter of the circle, then the angle opposite that side (the angle subtended by the diameter) is a right angle (90 degrees). In circle \( O \) with diameter \( QS \), triangles \( QTS \) and \( QUS \) are inscribed in the circle with \( QS \) as the diameter.

Step2: Apply Thales' theorem to \( \angle QTS \)

For triangle \( QTS \), since \( QS \) is the diameter of circle \( O \) and \( T \) is a point on the circle, by Thales' theorem, \( \angle QTS = 90^\circ \).

Step3: Apply Thales' theorem to \( \angle QUS \)

For triangle \( QUS \), since \( QS \) is the diameter of circle \( O \) and \( U \) is a point on the circle, by Thales' theorem, \( \angle QUS = 90^\circ \).

Answer:

\( \angle QTS = 90^\circ \), \( \angle QUS = 90^\circ \)