Answer:
The angle measured in degrees the corresponds to
of a circle is
![\bold{252^(\circ)}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/rpdimkut2ctqplf866nnler56gvv0t6l6l.png)
Solution:
The total angle present in a circle is
![\bold{360^(\circ)}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/1je8trs5w57a2s8b09rb56gxrrehk0nisi.png)
Any portion of circle be the part of that
![360^(\circ)](https://img.qammunity.org/2020/formulas/mathematics/high-school/fo7gb1usu0tkyyqujnlmxjjyiyxlze090t.png)
Let x be the portion in circle, the corresponding angle measurement =
![(x)/(360)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/axzxsnjo8ox3ubg2pi05hu95qiab7x9ej9.png)
Given portion is x =
![(7)/(10)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/rx7uu4995jmld2457yw4kncm86qrlnpy50.png)
Respective angle =
![(7)/(10) * 360](https://img.qammunity.org/2020/formulas/mathematics/middle-school/whdeiptvcpkjw6toyo9w378ed2j6y9kjt2.png)
![=7 * 36 = 252^(\circ)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/uvi969ck9425h1qpuxpowesgtmss8hhtny.png)
Hence the angle measured in degrees that corresponds to
of a circle is
![\bold{252^(\circ)}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/rpdimkut2ctqplf866nnler56gvv0t6l6l.png)