MATH SOLVE

3 months ago

Q:
# HELP NEED NOW, WILL GIVE BRAINLIEST: The difference of measures between the arcs subtended by chord AB is 160°. Line l is tangent to the circle at point A. Find the measure of the angle between the tangent l and secant AB.

Accepted Solution

A:

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°_____Comment on this geometryConsider 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 l, and you have the geometry shown here.