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

48 degrees

Explanation:

Just took the test! Hope it helps

Answer 2

Answer:
`mArc\ FH=48\°`

Explanation:

The missing figure is attached.

Observe the figure.

By definition:

`m\angle BDE=(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\°=(1)/(2)(mArc\ AJ- 38\°)\\\\2(37\°)+38\°=mArc\ AJ\\\\mArc\ AJ=112\°`

By definition:

`m\angle FGH=(1)/(2)(mArc\ AJ- mArc\ FH)`

Since:

`m\angle FGH=32\°`

You can substitute values and solve for the Arc FH:

`32\°=(1)/(2)(112\°- mArc\ FH)\\\\2(32\°)-112\°=-mArc\ FH\\\\mArc\ FH=48\°`