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

Answer:

The variable is 8/7.

Step-by-step 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

$\angle C=\frac{1}{2}arcAB$

Replacing each expression

$-x+8=\frac{1}{2}(12x)\\ -x=6x-8\\8=x+6x\\7x=8\\x=\frac{8}{7}$

Therefore, the variable is 8/7.

Answer 2

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

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