In the figure below, $\overline{A C}$ and $\overline{B D}$ are diameters of circle $P$.
What is the arc measure of major arc $B \overparen{D} C$ in degrees?

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∻Solution by Steps∻ ‖ step 1 ⋮ Combine like terms in the equation $4k + 159 + 2k + 153 = 360$. ‖ ‖ step 2 ⋮ Simplify to get $6k + 312 = 360$. ‖ ‖ step 3 ⋮ Subtract 312 from both sides to isolate the term with $k$, resulting in $6k = 48$. ‖ ‖ step 4 ⋮ Divide both sides by 6 to solve for $k$, yielding $k = 8$. ‖ ‖ step 5 ⋮ Substitute $k = 8$ into the angle $APC$ to find its measure: angle $APC = 4k + 159$. ‖ ‖ step 6 ⋮ Calculate the measure of angle $APC$ by substituting $k = 8$: angle $APC = 4(8) + 159 = 32 + 159 = 191$ degrees. ‖ ‖ step 7 ⋮ Since $AC$ is a diameter, angle $APC$ intercepts a semicircle, and thus the arc measure of $B\overparen{D}C$ is $360 - 191 = 169$ degrees. ‖ ∻[question 1] Answer∻ ⚹ The arc measure of major arc $B \overparen{D} C$ is $169$ degrees. ⚹ ∻Key Concept∻ ⚹Intercepted Arc by a Central Angle⚹ ∻Explanation∻ ⚹The measure of an arc intercepted by a central angle is equal to the measure of the angle itself. Since angle $APC$ intercepts a semicircle, the remaining arc $B\overparen{D}C$ is the difference between $360$ degrees and the measure of angle $APC$.⚹◊What is the relationship between the central angle and the arc measure of a circle segment in degrees?⍭ Generate me a similar question◊

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