Answer:
• 259 degrees
,
• 112.56m
,
• 56.28m
Explanation:
In the circle:
[tex]\text{mArc ADC}\cong\text{mArc BDC}[/tex]
The sum of the angle in a circle = 360 degrees
[tex]\begin{gathered} \widehat{}\widehat{\text{ADC}}\text{+}\widehat{B\text{DC}}\text{+}\widehat{A\text{DB}}=360\degree \\ \widehat{\text{ADC}}\text{+}\widehat{B\text{DC}}\text{+}101\degree=360\degree \\ 2\times\widehat{B\text{DC}}\text{+}101\degree=360\degree \\ 2\times\widehat{B\text{DC}}=360\degree-101\degree \\ 2\times\widehat{B\text{DC}}=259\degree \\ \widehat{B\text{DC}}=\frac{259\degree}{2} \\ \widehat{\text{ADC}}=\widehat{B\text{DC}}=129.5\degree \end{gathered}[/tex]
Part 8
The measure of arc ACB.
[tex]\begin{gathered} \text{ }\widehat{ACB}=360\degree-101\degree \\ =259\degree \end{gathered}[/tex]
Part 9
Length of arc ACB
[tex]\begin{gathered} \text{Length of an arc=}\frac{\theta}{360\degree}\times2\pi r \\ \theta=\text{central angle} \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} \text{Length of }\widehat{ACB}=\frac{259\degree}{360\degree}\times2\times\pi\times24.9 \\ =112.56m \end{gathered}[/tex]
Part 10
Length of arc CB.
The central angle subtended by CB = 129.5 degrees
Therefore:
[tex]\begin{gathered} \text{Length of }\widehat{CB}=\frac{129.5\degree}{360\degree}\times2\times\pi\times24.9 \\ =56.28m \end{gathered}[/tex]
