Question

Given: m

Answer 1

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 2

Answer:

m∠LTE = 110°

Step-by-step explanation:

We know that sum of all arcs of a circle is 360°

Therefore $m(arcAL)+m(arcLG)+m(arcGF)+(mFE)=360$

Now we put the values of each arc

$(2x)+(3x)+(4x-8)+(x-12)=2x+3x+4x+x-8-12=10x-20=360$

10x = 360 + 20

10x = 380

$x=\frac{380}{10}$

x = 38

Now from the theorem of intersecting chords in a circle

Measure of ∠LTE = $\frac{1}{2}[m(arcEL)+m(arcGF)]$

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 = $\frac{1}{2}(76 + 144)=\frac{220}{2}=110$

Therefore m∠LTE = 110° is the answer.