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In OP, mBC = 150°, mDE = 40°, mEF = 50°, mFB = 60°. Find each measure.
E
D
mZBCA=
mZFHCE
m2A=
mZGBC =
measure of arc EBC =

Content Common In OP mBC 150 mDE 40 mEF 50 mFB 60 Find each measure E D mZBCA mZFHCE m2A mZGBC measure of arc EBC class=

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sqdancefan

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Answer:

  • ∠BCA = 30°
  • ∠FHC = 125°
  • ∠A = 45°
  • ∠GBC = 75°
  • arc EBC = 260°

Step-by-step explanation:

Angle BCA intercepts arc FB, so is half its measure: 60°/2 = 30°.

Angle FHC is half the sum of the angles intercepted by its chords: (60°+150°+40°)/2 = 125°.

Angle A is half the difference of the arcs it intersects: (150° -60°)/2 = 45°.

Angle GBC is half the measure of the arc it intercepts: 150°/2 = 75°.

arc EBC is the sum of arcs EF, FB, and BC: 50° +60° +150° = 260°.

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