Question

I need help to Find / solve for x. I know it’s easy but I can’t remember how with degrees.

Answer 1

Explanation

We are given the following information from the image:

• m∠EGF = 31x + 3

,

• Arc angle = 192°

We are required to determine the value of x.

We know that the angle subtended by the arc at the center of the circle is the angle of the arc. Therefore, we have:

`\begin{gathered} m\angle EGF=31x+3 \\ m\angle EOF=192\degree \\ where\text{ }O\text{ }is\text{ }the\text{ }center\text{ }of\text{ }the\text{ }circle \end{gathered}`

We also know that one of the circle theorems states that the angle subtended by an arc at the center is twice the angle subtended at the circumference. This becomes:

`\begin{gathered} m\angle EOF=2* m\angle EGF \\ 192\degree=2(31x+3) \\ 192\degree=62x+6 \\ 62x=192-6 \\ 62x=186 \\ (62x)/(62)=(186)/(62) \\ x=3 \end{gathered}`

Hence, the value of x is 3.