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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

Respuesta :

luisejr77

Answer: [tex]mArc\ FH=48\°[/tex]

Step-by-step explanation:

The missing figure is attached.

Observe the figure.

By definition:

[tex]m\angle BDE=\frac{1}{2}(mArc\ AJ- mArc\ BE)[/tex]

You can identify that:

[tex]m\angle BDE=37\°\\\\mArcBE=38\°[/tex]

Substitute values and solve for the arc AJ:

[tex]37\°=\frac{1}{2}(mArc\ AJ- 38\°)\\\\2(37\°)+38\°=mArc\ AJ\\\\mArc\ AJ=112\°[/tex]

By definition:

[tex]m\angle FGH=\frac{1}{2}(mArc\ AJ- mArc\ FH)[/tex]

Since:

[tex]m\angle FGH=32\°[/tex]

You can substitute values and solve for the Arc FH:

[tex]32\°=\frac{1}{2}(112\°- mArc\ FH)\\\\2(32\°)-112\°=-mArc\ FH\\\\mArc\ FH=48\°[/tex]

Ver imagen luisejr77
48105Brown

Answer:

48 degrees

Step-by-step explanation:

Just took the test! Hope it helps

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