Answer:
LM = 1.5
LN = 3
Step-by-step explanation:
From the question given:
M is the midpoint of LN
LM = 3x
LN= 2x + 2
LM =.?
Next, we shall determine the value of x. This is illustrated below:
Since M is the midpoint of LN, it means that when we divide LN by 2 the result will be LM i.e
LN /2 = LM
With the above formula, we can obtain the value of x as follow:
LN= 2x + 2
LM = 3x
x =..?
LN /2 = LM
2x + 2/ 2 = 3x
Cross multiply
2 × 3x = 2x + 2
6x = 2x + 2
Collect like terms
6x - 2x = 2
4x = 2
Divide both side by 4
x = 2/4
x = 0.5
Finally, we can obtain LM and LN as follow:
LM = 3x
x = 0.5
LM = 3 × 0.5
LM = 1.5
LN= 2x + 2
x = 0.5
LN = 2(0.5) + 2
LN = 1 + 2
LN = 3
<h3>
Answer: 161 degrees</h3>
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Explanation:
Line AE is a tangent while line AU is a secant. The angle formed by the secant and tangent lines connects with the arcs through this formula
secant tangent angle = (larger arc - smaller arc)/2
More specifically, we can say:
angle EAI = (arc EU - arc IE)/2
42 = ( (7m+5) - (3m-1) )/2
42*2 = (7m+5) - (3m-1)
84 = 7m+5 - 3m+1
84 = 4m+6
4m+6 = 84
4m = 84-6
4m = 78
m = 78/4
m = 39/2
m = 19.5
Use this value of m to compute each arc
- arc IE = 3m-1 = 3*19.5-1 = 57.5 degrees
- arc EU = 7m+5 = 7*19.5+5 = 141.5 degrees
Let's say arc IU is some unknown number x. It must add to the other two arc measures to form 360 degrees, which is a full circle.
(arc IU) + (arc IE) + (arc EU) = 360
x + 57.5 + 141.5 = 360
x + 199 = 360
x = 360-199
x = 161
The measure of minor arc IU is 161 degrees
the length for each remaining side is 69 inches
