In the figure below, $${A B}$$ is a diameter of circle $$P$$. What is the arc measure of major arc $${A B C}$$ on circle $$P$$ in degrees?

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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>In the figure below, $${A B}$$ is a diameter of circle $$P$$. What is the arc measure of major arc $${A B C}$$ on circle $$P$$ in degrees?

![](http://admin.getprephub.com/media/editor/ci3_20230216203108930037.png)</textarea>In the figure below, <math><semantics><mrow><mrow><mi>A</mi><mi>B</mi></mrow></mrow><annotation encoding="application/x-tex">{A B}</annotation></semantics></math>AB is a diameter of circle <math><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math>P. What is the arc measure of major arc <math><semantics><mrow><mrow><mi>A</mi><mi>B</mi><mi>C</mi></mrow></mrow><annotation encoding="application/x-tex">{A B C}</annotation></semantics></math>ABC on circle <math><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math>P in degrees?
<img src="http://admin.getprephub.com/media/editor/ci3_20230216203108930037.png" alt="">
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>$$A B$$ is the diameter of the circle.

The arc measure of major arc $${A B}$$ on circle $$P$$ in degrees $$=180^{\circ}$$

The arc measure of major arc $${A B C}$$ on circle $$P$$ in degrees

$$=180^{\circ}+$$ The arc measure of major arc $${B C}$$ on circle $$P$$ in degrees

$$=180^{\circ}+41^{\circ}=221^{\circ}$$ </textarea><math><semantics><mrow><mi>A</mi><mi>B</mi></mrow><annotation encoding="application/x-tex">A B</annotation></semantics></math>AB is the diameter of the circle.
The arc measure of major arc <math><semantics><mrow><mrow><mi>A</mi><mi>B</mi></mrow></mrow><annotation encoding="application/x-tex">{A B}</annotation></semantics></math>AB on circle <math><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math>P in degrees <math><semantics><mrow><mo>=</mo><mn>1</mn><mn>8</mn><msup><mn>0</mn><mrow><mo>∘</mo></mrow></msup></mrow><annotation encoding="application/x-tex">=180^{\circ}</annotation></semantics></math>=180​∘​​
The arc measure of major arc <math><semantics><mrow><mrow><mi>A</mi><mi>B</mi><mi>C</mi></mrow></mrow><annotation encoding="application/x-tex">{A B C}</annotation></semantics></math>ABC on circle <math><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math>P in degrees
<math><semantics><mrow><mo>=</mo><mn>1</mn><mn>8</mn><msup><mn>0</mn><mrow><mo>∘</mo></mrow></msup><mo>+</mo></mrow><annotation encoding="application/x-tex">=180^{\circ}+</annotation></semantics></math>=180​∘​​+ The arc measure of major arc <math><semantics><mrow><mrow><mi>B</mi><mi>C</mi></mrow></mrow><annotation encoding="application/x-tex">{B C}</annotation></semantics></math>BC on circle <math><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math>P in degrees
<math><semantics><mrow><mo>=</mo><mn>1</mn><mn>8</mn><msup><mn>0</mn><mrow><mo>∘</mo></mrow></msup><mo>+</mo><mn>4</mn><msup><mn>1</mn><mrow><mo>∘</mo></mrow></msup><mo>=</mo><mn>2</mn><mn>2</mn><msup><mn>1</mn><mrow><mo>∘</mo></mrow></msup></mrow><annotation encoding="application/x-tex">=180^{\circ}+41^{\circ}=221^{\circ}</annotation></semantics></math>=180​∘​​+41​∘​​=221​∘​​ 
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