select the correct answer. in the diagram, point m is the center of the circle. if m∠pmn = 134°, what is…

select the correct answer. in the diagram, point m is the center of the circle. if m∠pmn = 134°, what is m∠pon? a. 46° b. 67° c. 90° d. 134°

select the correct answer. in the diagram, point m is the center of the circle. if m∠pmn = 134°, what is m∠pon? a. 46° b. 67° c. 90° d. 134°

Answer

Explanation:

Step1: Recall the central - inscribed angle relationship

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc. Here, $\angle PON$ is an inscribed angle and $\angle PMN$ is a central angle, and they subtend the same arc $\overset{\frown}{PN}$.

Step2: Calculate the measure of $\angle PON$

Let $m\angle PON = x$ and $m\angle PMN=y$. We know that $y = 134^{\circ}$ and the formula is $x=\frac{y}{2}$. So $x=\frac{134^{\circ}}{2}=67^{\circ}$.

Answer:

B. $67^{\circ}$