Circle $$D$$ is below. What is the arc measure of minor arc $${B C}$$ in degrees?

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<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea wfd-invisible="true">Circle $$D$$ is below. What is the arc measure of minor arc $${B C}$$ in degrees?

![](http://admin.getprephub.com/media/editor/ci6_20230216203427850761.png)</textarea>Circle <math><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex" wfd-invisible="true">D</annotation></semantics></math>D is below. What is the arc measure of minor arc <math><semantics><mrow><mrow><mi>B</mi><mi>C</mi></mrow></mrow><annotation encoding="application/x-tex" wfd-invisible="true">{B C}</annotation></semantics></math>BC in degrees?
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea wfd-invisible="true">Solution

$$m&lt; A D C+m&lt; A D B+m&lt; B D C=360^{\circ}$$ 

Or, $$(13 n-16)+(7 n+12)+6 n=360$$ 

Or, $$26n-4=360$$

Or, $$26n=360+4$$

Or, $$=\frac{364}{26}=14$$

The arc measure of minor arc $${B C}$$ in degrees $$=6 n=6 \times 14=84^{\circ}$$</textarea>Solution
<math><semantics><mrow><mi>m</mi><mo>&lt;</mo><mi>A</mi><mi>D</mi><mi>C</mi><mo>+</mo><mi>m</mi><mo>&lt;</mo><mi>A</mi><mi>D</mi><mi>B</mi><mo>+</mo><mi>m</mi><mo>&lt;</mo><mi>B</mi><mi>D</mi><mi>C</mi><mo>=</mo><mn>3</mn><mn>6</mn><msup><mn>0</mn><mrow><mo>∘</mo></mrow></msup></mrow><annotation encoding="application/x-tex" wfd-invisible="true">m&lt; A D C+m&lt; A D B+m&lt; B D C=360^{\circ}</annotation></semantics></math>m&lt;ADC+m&lt;ADB+m&lt;BDC=360​∘​​ 
Or, <math><semantics><mrow><mo>(</mo><mn>1</mn><mn>3</mn><mi>n</mi><mo>−</mo><mn>1</mn><mn>6</mn><mo>)</mo><mo>+</mo><mo>(</mo><mn>7</mn><mi>n</mi><mo>+</mo><mn>1</mn><mn>2</mn><mo>)</mo><mo>+</mo><mn>6</mn><mi>n</mi><mo>=</mo><mn>3</mn><mn>6</mn><mn>0</mn></mrow><annotation encoding="application/x-tex" wfd-invisible="true">(13 n-16)+(7 n+12)+6 n=360</annotation></semantics></math>(13n−16)+(7n+12)+6n=360 
Or, <math><semantics><mrow><mn>2</mn><mn>6</mn><mi>n</mi><mo>−</mo><mn>4</mn><mo>=</mo><mn>3</mn><mn>6</mn><mn>0</mn></mrow><annotation encoding="application/x-tex" wfd-invisible="true">26n-4=360</annotation></semantics></math>26n−4=360
Or, <math><semantics><mrow><mn>2</mn><mn>6</mn><mi>n</mi><mo>=</mo><mn>3</mn><mn>6</mn><mn>0</mn><mo>+</mo><mn>4</mn></mrow><annotation encoding="application/x-tex" wfd-invisible="true">26n=360+4</annotation></semantics></math>26n=360+4
Or, <math><semantics><mrow><mo>=</mo><mfrac><mrow><mn>3</mn><mn>6</mn><mn>4</mn></mrow><mrow><mn>2</mn><mn>6</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mn>4</mn></mrow><annotation encoding="application/x-tex" wfd-invisible="true">=\frac{364}{26}=14</annotation></semantics></math>=​26​​364​​=14
The arc measure of minor arc <math><semantics><mrow><mrow><mi>B</mi><mi>C</mi></mrow></mrow><annotation encoding="application/x-tex" wfd-invisible="true">{B C}</annotation></semantics></math>BC in degrees <math><semantics><mrow><mo>=</mo><mn>6</mn><mi>n</mi><mo>=</mo><mn>6</mn><mo>×</mo><mn>1</mn><mn>4</mn><mo>=</mo><mn>8</mn><msup><mn>4</mn><mrow><mo>∘</mo></mrow></msup></mrow><annotation encoding="application/x-tex" wfd-invisible="true">=6 n=6 \times 14=84^{\circ}</annotation></semantics></math>=6n=6×14=84​∘​​
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