The expression which gives the measure of ∠RST, in the diagram where TS and RS are tangent to the circle is 1/2(162°-38°).
What is the theorem of two tangents from the external point?
When the two tangents are drawn to a circle from an exterior point then according to this theorem-
- The length of these two tangents is equal.
- Both the tangents subtend at equal angles at the centre of the circle.
- The angle between the two tangents is bisected by the line joining the exterior point and the centre.
In the diagram below, TS and RS are tangents to the circle. In the diagram half of the difference between the arc TR and UV is equal to the angle of the measure of RST. Thus,
∠RST=1/2(TR-UV)=1/2(162°-38°)
Thus, the expression which gives the measure of ∠RST, in the diagram where TS and RS are tangent to the circle is 1/2(162°-38°).
Learn more about the theorem of two tangents from an external point here:
https://brainly.com/question/23971197.
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