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Calculate the angles WRS and WRT.

May 13, 2026Mathematics

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Answer

\text{}90^\circ\text{}

2 steps

Here are the calculations for the angles:

1.2.1 Calculate WRS

Identify the relationship between the tangent and diameter.
RW is a tangent to the circle at R, and RS is the diameter. The angle between a tangent and a diameter at the point of contact is $90^\circ$ .
$\angle WRS = 90^\circ$
The size of WRS is $\boxed{\text{}90^\circ\text{}}$

1.2.2 Calculate W
Identify angles using the tangent-chord theorem and angle in a semicircle.
RW is a tangent and RT is a chord, so $\angle WRT = \angle RST$ (tangent-chord theorem).

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