Question

Angle C is an inscribed angle of circle P. Angle C measures (-x + 8) degrees and arc AB measures (12x) degrees. Find x

Answer 1

The rule for this is that the measure in degrees of the inscribed angle is half the measure of the arc in degrees. If angle C measures 8-x and arc AB measures 12x, then the formula to solve for x would be

`8-x=(1)/(2)(12x)`. Simplifying a bit gives us that 8 - x = 6x. Add x to both sides and we have 8 = 7x and x = 8/7.

Answer 2

The variable is 8/7.

Explanation:

Givens

`\angle C = -x+8\\arcAB=12x`

To solve this problem, we need to use the Inscribed Angle Theorem which states that an angle inscribed in a circle is half of the subtended arc.

Based on this theorem, we have

`\angle C=(1)/(2)arcAB`

Replacing each expression

`-x+8=(1)/(2)(12x)\\ -x=6x-8\\8=x+6x\\7x=8\\x=(8)/(7)`

Therefore, the variable is 8/7.