In the figure below, $${A C}$$ and $${B D}$$ are diameters of circle $$P$$. What is the arc measure of major arc $${B D C}$$ in degrees? ![](http://admin.getprephub.com/media/editor/ci9_20230216204133693485.png)

Solution $${A C}$$ and $${B D}$$ are diameters of circle $$P$$. $$m< B P C$$ and $$m < A P D$$ are vertically opposite angles. Therefore, $$m< B P C=m< A P D$$ Or, $$4 k+159=2 k+153$$ Or, $$4 {k}-2 {k}=153-159$$ Or. $$2 {k}=-6$$ Or, $${k}=-3$$ Again. $$m< A P B$$ and $$m< C P D$$ are vertically opposite angles. Hence, $$m< A P B=m< C P D$$ Also, $$m< A P D=2(-3)+153=153-6=147^{\circ}$$ We know that, $${m}< A D C=180^{\circ}$$ or, $${m}< A P D+m< D P C=180^{\circ}$$ or, $$147+m< D P C=180$$ or, $${m}< D P C=180-147=33^{\circ}$$ The arc measure of major arc $${B D C}$$ in degrees $$=m < B P D+m < D P C=180+33=213^{\circ}$$

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

Select all that apply :

$213^{\circ}$

$102^{\circ}$

$452^{\circ}$

$45^{\circ}$

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