Question

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 =

Answer 1

9514 1404 393

Answer:

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

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°.