Circle $${P}$$ is below. What is the arc measure of major arc $${A B C}$$ in degrees? ![](http://admin.getprephub.com/media/editor/ci7_20230216203828459111.png)

Solution We know that, $$m< B P C+m< A P B+m< A P C=360^{\circ}$$ Or, $$(4 y+6)+(20 y-11)+(7 y-7)=360$$ Or, $$31 y-12=360$$ Or, $$31y =372$$ Or, $$ y=12$$ The value of $${m}< A P C=7 \times 12-7=77^{\circ}$$ The arc measure of major arc $${A B C}$$ in degrees $$=360^{\circ}-m< A P C=360^{\circ}-77^{\circ}=283^{\circ}$$

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Circle ${P}$ is below. What is the arc measure of major arc ${A B C}$ in degrees?

Select all that apply :

$283^{\circ}$

$258^{\circ}$

$185^{\circ}$

$103^{\circ}$

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