in the figure below, $\\overline{ab}$ is a diameter of circle $p$.\nwhat is the arc measure of major arc…
in the figure below, $\\overline{ab}$ is a diameter of circle $p$.\nwhat is the arc measure of major arc $\\widehat{abc}$ in degrees?
Answer
Explanation:
Step1: Identify the measure of the semicircle
Since $AB$ is a diameter, the arc $AB$ (semicircle) is $180^{\circ}$. $$m\text{arc } AB = 180^{\circ}$$
Step2: Determine the measure of minor arc BC
The central angle $\angle BPC$ is $69^{\circ}$, so the arc $BC$ is $69^{\circ}$. $$m\text{arc } BC = 69^{\circ}$$
Step3: Calculate the measure of major arc ABC
The major arc $ABC$ consists of the semicircle $AB$ plus arc $BC$. $$m\text{arc } ABC = m\text{arc } AB + m\text{arc } BC$$
Step4: Perform the addition
Substitute the values into the equation. $$180^{\circ} + 69^{\circ} = 249^{\circ}$$
Answer:
249^{\circ}