Question

in the figures below, circle p is congruent to circle t and \\(\overarc{rs} \cong \overarc{gh}\\). determine \\(\overarc{rs}\\).

Explanation:

Step1: Set expressions equal

Since $\widehat{RS} \cong \widehat{GH}$, their measures are equal:
$10x - 8 = 6x + 12$

Step2: Solve for x

Subtract $6x$ and add 8 to both sides:
$10x - 6x = 12 + 8$
$4x = 20$
$x = \frac{20}{4} = 5$

Step3: Calculate $\widehat{RS}$

Substitute $x=5$ into $10x-8$:
$10(5) - 8$

Answer:

42