Applying the angles of intersecting chords theorem, the measure of arc EI is: 140°.
What is the Angles of Intersecting Chords Theorem?
Based on the angles of intersecting chords theorem, the measure of the vertical angle formed when two chords intersect equals half the sum of the measures of the intercepted arcs.
Given the following:
- m∠EXY = 80°
- m∠K = 25°
- m(EY) = m(YI)
m∠K = 1/2(2(EY) -m(JL))
25 = 1/2(2(m(EY)) -m(JL))
50 = 2(m(EY)) -m(JL)
m(JL) = 2(m(EY)) - 50
m∠EXY = 1/2(m(JL) + m(EY) [angles of intersecting chords theorem]
Substitute
80 = 1/2[2(m(EY)) - 50 + m(EY)]
2(80) = 2(m(EY)) - 50 + m(EY)
160 = 3(m(EY)) - 50
160 + 50 = 3(m(EY))
210 = 3(m(EY))
210/3 = m(EY)
m(EY) = 70°
m(EI) = 2(m(EY)) = 2(70)
m(EI) = 140°
Therefore, applying the angles of intersecting chords theorem, the measure of arc EI is: 140°.
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