Question

Calculate the Value of x.

Answer 1

`\large\boxed{\mathtt{x=44^(\circ)}}`

Explanation:

`\textsf{We are asked to find the value of x.}`

`\textsf{We should know that} \ \angle \textsf{CAB is an Interior Angle.}`

`\large\underline{\textsf{What is an Interior Angle?}}`

`\textsf{An Interior Angle is any angle that is inside of a circle. It's formed by 2 Chords.}`

`\large\underline{\textsf{What is a Chord?}}`

`\textsf{A Chord is any line segment inside of a circle. Its' endpoints are on the circumference.}`

`\textsf{Because Interior Angles are formed by Chords, the arc within its endpoints is}`

`\textsf{half of the measurement of the Interior Angle.}`

`\large\underline{\textsf{For this problem;}}`

`\mathtt{x=(1)/(2) \widehat{BC}}`

`\textsf{We can't find x right away. We should find} \ \mathtt{ \widehat{BC}} \ \textsf{first.}`

`\textsf{We are given} \ \mathtt{\widehat{AC} = 92^(\circ).}`

`\textsf{The Arcs around a circle add up to 360}^(\circ).`

`\overline{AB} \ \textsf{is a diameter. The arc will equal 180}^(\circ).`

`\large\underline{\textsf{Solve for BC;}}`

`\mathtt{92^(\circ)+180^(\circ)+\widehat{BC} = 360^(\circ).}`

`\large\underline{\textsf{Combine Like Terms:}}`

`\mathtt{272^(\circ)+\widehat{BC} = 360^(\circ).}`

`\large\underline{\textsf{Subtract 272 from both sides of the equation:}}`

`\mathtt{\widehat{BC} = 88^(\circ).}`

`\large\underline{\textsf{Remember that;}}`

`\mathtt{x=(1)/(2) \widehat{BC}}`

`\large\underline{\textsf{Substitute:}}`

`\mathtt{x=(1)/(2) (88^(\circ))}`

`\large\underline{\textsf{Multiply:}}`

`\large\boxed{\mathtt{x=44^(\circ)}}`