I need to know how to find the measure of the arc or central angles indicated

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asked Nov 28, 2023 233k views

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BrenBarn · Answer 1 · 2023-12-02T15:34:23+0000

The sum of angles at a point (or in a circle) is 360 degrees.

Therefor, we have that:

$m\angle GCD+m\operatorname{\angle}DCE+m\operatorname{\angle}ECF+m\operatorname{\angle}FCG=360\degree$

Given the values in the question:

$\begin{gathered} m\operatorname{\angle}DCE=75 \\ m\operatorname{\angle}ECF=80 \\ m\operatorname{\angle}FCG=55 \end{gathered}$

Therefor, we can calculatoe the measure of angle GCD to be:

$\begin{gathered} m\operatorname{\angle}GCD+75+80+55=360 \\ m\operatorname{\angle}GCD=360-75-80-55 \\ m\operatorname{\angle}GCD=150\degree \end{gathered}$

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I need to know how to find the measure of the arc or central angles indicated

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