Answer:
m∠LTE = 110
Step-by-step explanation:
1. add up all of the arcs.
2x+3x+4x-8+x-12
2. all of the arcs equal 360
2x+3x+4x-8+x-12=360
3. Find x
10x-20=360, x=38
4. angle LTE is equal to half of the sum of the intercepted arcs.
0.5(arc LE +GF)
5. plug in LE +GF with x
.5(76+144)
Answer:
m∠LTE = 110°
Step-by-step explanation:
We know that sum of all arcs of a circle is 360°
Therefore [tex]m(arcAL)+m(arcLG)+m(arcGF)+(mFE)=360[/tex]
Now we put the values of each arc
[tex](2x)+(3x)+(4x-8)+(x-12)=2x+3x+4x+x-8-12=10x-20=360[/tex]
10x = 360 + 20
10x = 380
[tex]x=\frac{380}{10}[/tex]
x = 38
Now from the theorem of intersecting chords in a circle
Measure of ∠LTE = [tex]\frac{1}{2}[m(arcEL)+m(arcGF)][/tex]
m(arc EL) = 2x = 2×38 = 76°
m(arc GF) = (4x - 8) = (4×38 - 8) = (152 - 8) = 144°
Now we can get the measure of ∠LTE
m∠LTE = [tex]\frac{1}{2}(76 + 144)=\frac{220}{2}=110[/tex]
Therefore m∠LTE = 110° is the answer.
