Given:
Circle with center O.
To find:
The measurement of the angle GHJ.
Solution:
The arc measure of full circle is 360°.
m(ar GJ) + m(ar JI) + m(ar IH) + m(ar HG) = 360°
m(ar GJ) + 115° + 31° + 68° = 360°
m(ar GJ) + 214° = 360°
Subtract 214° from both sides.
m(ar GJ) + 214° - 214°= 360° - 214°
m(ar GJ) = 146°
The measure of inscribed angle is half the intercepted arcs.
[tex]$\Rightarrow m\angle GHJ = \frac{1}{2} m(ar \ GJ)[/tex]
[tex]$\Rightarrow m\angle GHJ = \frac{1}{2} (146^\circ)[/tex]
[tex]$\Rightarrow m\angle GHJ =73^\circ[/tex]
The measure of angle GHJ is 73°.
