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Circle Y is shown. Chords R T and S U intersect at point Z. Arc S R is 100 degrees and arc T U is 72 degrees. In circle Y, what is m∠SZT?

Respuesta :

Answer:

m∠SZT = 86°

Step-by-step explanation:

First we draw the diagram from the given information. Find attached the diagram.

when two chords intersect inside a circle, the measure of the angle formed is 1/2(the sum of the measure of the arcs intercepted each other).

From the above,

m∠SZT = 1/2 (Arc SR + arc TU)

Arc SR =100 degrees

Arc TU =72 degrees

m∠SZT = 1/2 (100° + 72°)

m∠SZT = 1/2 (172°)

m∠SZT = 86°

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abidemiokin

These are circles that include lines and angles. The measure of angle m∠SZT from the given diagram is 86°

Coordinate geometry

These are circles that include lines and angles. Using the theorem, the measure of the vertex is half that of its intercepted arc.

Based on the theorem;

m∠SZT = 1/2 (arcSR + arcTU)

Given

Arc SR =100 degrees

Arc TU =72 degrees

Substitute

m∠SZT = 1/2 (100° + 72°)

m∠SZT = 1/2 (172°)

m∠SZT = 86°

The measure of angle m∠SZT from the given diagram is 86°

Learn more on coordinate geometry here: https://brainly.com/question/18269861

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