Question

Circle C is shown. Secants A D and D J intersects at point D outside of the circle. Secant A D intersects the circle at point B and secant D J intersects the circle at point E. Angle D is 37 degrees and the measure of arc B E is 38 degrees. Secants A G and J G intersect at point G outside of the circle. Secant A G intersects the circle at point F and secant J G intersects the circle at point H. Angle G is 32 degrees.
In circle C, what is mArc F H?


31°

48°

112°

121

Answer 1

Answer: $mArc\ FH=48\°$

Step-by-step explanation:

The missing figure is attached.

Observe the figure.

By definition:

$m\angle BDE=\frac{1}{2}(mArc\ AJ- mArc\ BE)$

You can identify that:

$m\angle BDE=37\°\\\\mArcBE=38\°$

Substitute values and solve for the arc AJ:

$37\°=\frac{1}{2}(mArc\ AJ- 38\°)\\\\2(37\°)+38\°=mArc\ AJ\\\\mArc\ AJ=112\°$

By definition:

$m\angle FGH=\frac{1}{2}(mArc\ AJ- mArc\ FH)$

Since:

$m\angle FGH=32\°$

You can substitute values and solve for the Arc FH:

$32\°=\frac{1}{2}(112\°- mArc\ FH)\\\\2(32\°)-112\°=-mArc\ FH\\\\mArc\ FH=48\°$