Applying the angles of intersecting chords theorem, m∠LTE = 110°.
What is the Angles of Intersecting Chords Theorem?
When two chords intersect inside a circle, according to the angles of intersecting chords theorem, the vertical angle formed equals the half the sum of the measures of the intercepted arcs.
Given the following:
- EL=(2x)°
- LG=(3x)°
- GF=(4x−8)°
- FE=(x−12)°
A full circle = 360°
Therefore we would have:
2x + 3x + 4x - 8 + x - 12 = 360
Add like terms
10x - 20 = 360
10x = 360 + 20
10x = 380
x = 38
Based on the angles of intersecting chords theorem, we have:
m∠LTE = 1/2(EL + GF)
Substitute
m∠LTE = 1/2(2x + 4x - 8)
m∠LTE = 1/2(6x - 8)
Plug in the value of x
m∠LTE = 1/2(6(38) - 8)
m∠LTE = 1/2(220)
m∠LTE = 110°
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