Question

find m\\(\widehat{ac}\\). show your work. drag the expressions into the boxes to correctly complete the solution. hide hints recall that m\\(\angle apc\\) = \\(\frac{1}{2}(m\widehat{ac}+m\widehat{bd})\\). m\\(\angle apc\\) = \\(\frac{1}{2}\\) = \\(\frac{1}{2}\\) = = m\\(\widehat{ac}\\)

Explanation:

Step1: Identify given values

We know that $\angle APC = 125^{\circ}$ and $m\overparen{BD}=165^{\circ}$. The formula is $m\angle APC=\frac{1}{2}(m\overparen{AC}+m\overparen{BD})$.

Step2: Substitute values into formula

$125^{\circ}=\frac{1}{2}(m\overparen{AC} + 165^{\circ})$

Step3: Multiply both sides by 2

$2\times125^{\circ}=m\overparen{AC}+165^{\circ}$
$250^{\circ}=m\overparen{AC}+165^{\circ}$

Step4: Solve for $m\overparen{AC}$

$m\overparen{AC}=250^{\circ}- 165^{\circ}$
$m\overparen{AC}=85^{\circ}$

Answer:

$85^{\circ}$