In the figure below, $${X Z}$$ is a diameter of circle $${A}$$. What is the arc measure of minor arc $${Y Z}$$ in degrees? ![](http://admin.getprephub.com/media/editor/c8_20230403191452925358.png)

Solution $${X Z}$$ is a diameter of circle $${A}$$. $$m<X A Z=180^{\circ}$$ Or, $$m<X A Y+m<Y A Z=180^{\circ}$$ Or, $$11 w+5 w+4=180$$ Or, $$16w=180-4$$ Or, $$16 w=176$$ Or,$$ w = 11$$ The arc measure of minor $${arc}{Y Z}$$ in degrees $$=5 w+4=5 \times 11+4=59^{\circ}$$

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MCQ

In the figure below, ${X Z}$ is a diameter of circle ${A}$ . What is the arc measure of minor arc ${Y Z}$ in degrees?

Select all that apply :

$59^{\circ}$

$56^{\circ}$

$76^{\circ}$

$120^{\circ}$

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