Applying the definition of an angle bisector, the value of x is: 11.
<h3>What is an Angle Bisector?</h3>
When a line segment bisects an angle into two equal halves, it is called an angle bisector. The two small angles formed have equal measure.
Given that CH is the angle bisector of angle DHG
m(GF) = (2x + 6)°
m(DC) = (7x – 1)°
m(DC) = m(GC) = (2x + 6)° [congruent angle]
The measure of half a circle is 180 degrees.
Therefore, we would have the following equation that would enable us find the value of x:
2[m(DC)] + m(GF) = 180°
Plug in the values
2(7x – 1)° + (2x + 6)° = 180°
14x – 2 + 2x + 6 = 180
Combine like terms together
16x + 4 = 180
16x = 180 - 4
16x = 176
Divide both sides by 16
16x/16 = 176/16
x = 11
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