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3 years ago

Line segment TS is tangent to circle O at point N.

Mathematics

1 answer:

garik1379 [7]3 years ago

7 0

Answer:

148°

Step-by-step explanation:

The measure of the intercepted arc QN is twice the measure of inscribed angle QNT.

arc QN = 2(74°) = 148°

_____

<em>Comment on the question and answer</em>

Your description "on the circle between points Q and N" is ambiguous. You used the same description for both points P and R. The interpretation we used is shown in the attachment. If point P is on the long arc NQ, then the measure of arc QPN will be the difference between 148° and 360°, hence 212°. You need to choose the answer that matches the diagram you have.

We call angle QNT an "inscribed angle" because it is a degenerate case of an inscribed angle. The usual case has the vertex of the angle separate from the ends of the arc it intercepts. In the case of a tangent meeting a chord, the vertex is coincident with one of the ends of the intercepted arc. The relation between angle measure and arc measure remains the same: 1 : 2.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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