SOLUTION: Angle C is an inscribed angle of circle P. Angle C measures (20x � 5)� and arc AB measures (30x + 30)�. Find the measure of Angle C

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Question 965085: Angle C is an inscribed angle of circle P. Angle C measures (20x � 5)� and arc AB measures (30x + 30)�. Find the measure of Angle C
Answer by Theo(13342) (Show Source):
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the number of degrees in an inscribed angle is equal to 1/2 times the number of degrees in the inscribed arc formed by that angle.

for example:

if the number of degrees in the inscribed arc is 180, then the inscribed angle measures 90 degrees.

if the number of degrees in the inscribed arc is 90, then the inscribed angle measures 45 degrees.

your inscribed angle measures (20x - 5) degrees.

your inscribed arc created from that angle measures (30x + 30) degrees.

based on the formula that the inscribed angle measures 1/2 * the inscribed angle, 20x - 5 degrees is equal to 1/2 * 30x + 30 degrees.

your equation is:

20x - 5 = 1/2 * (30x + 30)

simplify to get 20x - 5 = 15x + 15

subtract 15x from both sides of this equation and add 5 to both sides of the equation to get:

20x - 15x = 15 + 5

simplify to get:

5x = 20

divide both sides of this equation by 4 to get:

x = 4.

your inscribed angle measures 20*4 - 5 degrees which is equal to 75 degrees.

your inscribed arc measures 30*4 + 30 which is equal to 150 degrees.

75 degrees is equal to 1/2 * 150 degrees so the solution looks good.