Angles at the center of a circle add up to 360 degrees.
The measure of angle GEH in the circle is (d) 116 degrees
The given parameters are:
[tex]\mathbf{\angle FEG = 64^o}[/tex]
Since line FH is the diameter of the circle;
It means that:
[tex]\mathbf{\angle FEG + \angle GEH = 180^o}[/tex] --- By angle on a straight line theorem
Substitute 64 for FEG
[tex]\mathbf{64 + \angle GEH = 180^o}[/tex]
Subtract 64 from both sides
[tex]\mathbf{\angle GEH = 180^o - 64}[/tex]
Evaluate like terms
[tex]\mathbf{\angle GEH = 116^o}[/tex]
Hence, the measure of angle GEH in the circle is (d) 116 degrees
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