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Can someone help me pls

Can someone help me pls-example-1
User Ju
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1 Answer

2 votes

Answer:


\boxed{ m \overset{\huge\frown}{EFC} \: = \: 237°}

Step-by-step explanation:

Assuming that
\overline{CF} is a diameter, and that the angle of an arc subtending the central angle is congruent,
m \overset{\Large\frown}{CGF} \: = \: 180°.

And according to the arc addition postulate,
\overset{\Large\frown}{CG} + \overset{\Large\frown}{GF} \: = \: \overset{\huge\frown}{CGF}.

Using the substitution property:


\overset{\Large\frown}{CG} + \overset{\Large\frown}{GF} \: = \: 180°.

Given that
m\overset{\Large\frown}{CG} \: = \: 140°.

Using the substitution property and that the measures apply to the arc addition postulate,
140° + m\overset{\Large\frown}{GF} \: = \: 180°.


140° – \: 140° + m\overset{\Large\frown}{GF} \: = \: 180° – \: 140°.


m\overset{\Large\frown}{GF} \: = \: 40°.

Since
\overset{\Large\frown}{GF} and
\overset{\Large\frown}{CD} are subtending the center of the circle, they form vertical angles and are therefore congruent.


\overset{\Large\frown}{GF} \: \cong \: \overset{\Large\frown}{CD}

According to the definition of a vertical angle,
m \overset{\Large\frown}{CD} \: = \: 40°.

Using the arc addition postulate again,


\overset{\Large\frown}{CD} + \overset{\Large\frown}{DE} + \overset{\Large\frown}{EF} \: = \:\overset{\huge\frown}{CDF}/\overset{\huge\frown}{CEF}

Using substitution, as well as how we are given that the central angle subtended by
\overset{\Large\frown}{DE} = 83°, we can find that:


40° + 83° + \overset{\Large\frown}{EF} \: = \:\overset{\huge\frown}{CDF}/\overset{\huge\frown}{CEF}

User Ivan Vinogradov
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