Question

Line segment XY is tangent to circle Z at point U. Circle Z is shown. Line segment U V is a secant. Line segment X Y is a tangent and intersects the circle at point U. The measure of arc U V is 84 degrees. If the measure of Arc U V is 84°, what is the measure of Angle Y U V?

Answer 1

Answer:

the measure of Angle Y U V is 42°.

Step-by-step explanation:

Do not answer if you do not know the correct answer. Simple as that.

-Ron

Answer 2

∠YUV  = 138° or 42°

Step-by-step explanation:

Line segment XY is tangent to circle Z at point U

Let say O is center of circle

=> ∠YUO  = 90°

The measure of arc U V is 84 degrees

=> ∠UOV = 84°

OU = OV  = radius

=> ∠OVU = ∠OUV

in Δ UOV

∠OVU +  ∠OUV + ∠UOV  = 180°

=> ∠OUV  + ∠OUV  + 84° = 180°

=> 2  ∠OUV  = 96°

=> ∠OUV  = 48°

∠YUV  = ∠YUO  ± ∠OUV   ( Depnding on position )

=> ∠YUV  = 90°  ± 48°

=> ∠YUV  = 138° or 42°

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