a. Applying the angle of intersecting chord theorem, m∠AEB = 57°.
b. Applying the , angle of intersecting tangents or secants theorem, VW = 106°.
<h3>What is the Angle of Intersecting Chords Theorem?</h3>
According to the angle of intersecting chord theorem, the angle formed inside a circle (i.e. angle AEB) by two chords (i.e. AC and BD) have a measure that is equal to half of the sum of the measures of intercepted arcs AB and CD.
<h3>What is the Angle of Intersecting Tangents or Secants Theorem?</h3>
According to the angle of intersecting tangents or secants theorem, the angle formed outside a circle (i.e. angle VZW) have a measure that is equal to half of the positive difference of the measures of intercepted arcs XY and VW.
a. m∠AEB = 1/2(measure of arc AB + measure of arc CD) [angle of intersecting chord theorem]
Substitute
m∠AEB = 1/2(53 + 61)
m∠AEB = 57°
b. 35 = 1/2(VW - 36) [angle of intersecting tangents or secants theorem]
Multiply both sides by 2
2(35) = VW - 36
70 = VW - 36
Add 36 to both sides
70 + 36 = VW
VW = 106°
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