Angles of intersecting chords theorem.

Formula for angles and intercepted arcs of intersecting chords.

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Angles formed by intersecting Chords

Use the thoerem for intersecting chordsto find the value of sum of intercepted arcs (assume all arcs to be minor arcs).

 Answer 
By our theorem, we know that
x = ½(arc TG + arc ER)
x =½(75 + 65)
x =½(140)
x = 70°

Use the thoerem for intersecting chordsto find the value of sum of intercepted arcs (assume all arcs to be minor arcs).

 sum of arcs  
By our theorem, we know that
110° = ½(arc TE + arc GR)
2 •( 110° = ½( TE + GR))
220° = (arc TE + arc GR)
Therefore the sum of them easures of minor arcs TE and GR is 220 °.

Find the is the measure of AEB and CED

 Measure of Angles  



AEB = ½(arc AB + arc CD)
AEB = ½(30° + 25°)
AEB = ½(55°)
AEB = 27.5°
mAEB = mCED since they are vertical angles.

What is wrong with this problem, based on the picture below and the measurements on the left?
 Answer 


The problem with these measurments is that if angle AEC = 70°, then we know that arc ABC + arc DF should equal 140°. Therefore, the sum of the two remaining arcs, arc ABC and arc AGF should equal 360°- 140°= 220°.
So far everything is fine.
However, the measurements of arcs AGF and CD do not add up to 220 °

170 + 40 ≠220

Therefore, the measurments provided in this problem violate the theoream that angles formed by intersecting arcs equals teh sum of the intercepted arcs.