<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 missing words to complete the proof are respectively; Vertical Angles; Corresponding angles; Transitive Property
<h3>How to prove congruent angles?</h3>
The image of the transversal line is attached.
1) We know that lines a and b are parallel and that line c is a transversal because that is given.
2) We can tell that angles 2 and 5 are congruent because vertical angles are congruent.
3) Angles 5 and 7 are congruent because corresponding angles by parallel lines cut by a transversal are congruent.
4) Therefore, angles 2 and 7 are congruent based on the transitive property.
Read more about Congruent Angles at; brainly.com/question/1675117
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Answer:
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Step-by-step explanation:
That's the right answer
