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Sunny_sXe [5.5K]
2 years ago
9

HELP NEED NOW, WILL GIVE BRAINLIEST: The difference of measures between the arcs subtended by chord AB is 160°. Line l is tangen

t to the circle at point A. Find the measure of the angle between the tangent l and secant AB.

Mathematics
1 answer:
omeli [17]2 years ago
4 0

Answer:

  50°

Step-by-step explanation:

As usual, the diagram is not drawn to scale.

The chord divides the circle into two arcs that have a sum of 360°. If we let "a" represent the measure of the smaller arc, then we have ...

  a + (a+160°) = 360°

  2a = 200° . . . . . . . . . . . subtract 160°

  a = 100°

The measure of the angle at A is 1/2 the measure of the subtended arc:

  acute ∠A = a/2 = (1/2)·100° = 50°

_____

<em>Comment on this geometry</em>

Consider a different inscribed angle, one with vertex V on the circle and subtending the same short arc subtended by chord AB. Then you know that the angle at V is half the measure of arc AB. This is still true as point V approaches (and becomes) point A on the circle. When V becomes A, segment VA becomes tangent line <em>l</em>, and you have the geometry shown here.

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