HELPPPPPPPPP ! In circle O, what is measure of Arc AE? A. 84 B. 96 C. 120 D. 168 BTW I HAVE MORE QUESTIONS UP IF YOU WANT TO HEL
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<h3>Answer: 73</h3>
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Work Shown:
Check out the diagram below. Note the pair of alternate interior angles that are congruent (each 37 degrees). Then focus on triangle ABC. With the reference angle being at A, this means we use the tangent function because BC = x is the opposite side and AB = 97 is the adjacent side.
tan(angle) = opposite/adjacent
tan(A) = BC/AB
tan(37) = x/97
97*tan(37) = x
x = 97*tan(37)
x = 73.094742859971
For the last step, you'll need a calculator that can handle trig functions. Make sure the calculator is in degree mode. The result here is approximate. This rounds to 73 when rounding to the nearest whole number.
From the markings on the diagram, we can tell E is the midpoint of BC and <u>D</u> is the midpoint of AC. We can apply the <u>triangle midsegment theorem</u>: ED = ½BA. Substituting in the expressions for the lengths and solving for x, we get x = <u>5</u>. Now, since BE = x, then BC = <u>10</u>.
<h3>What is triangle midpoint theorem?</h3>Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.
By applying the triangle midpoint theorem, we can find the value of x:
ED = ½BA
x + 2 = ½(4x - 6)
2x + 4 = 4x - 6
4x - 2x = 6 + 4
2x = 10
x = 10/2
x = 5.
BC = x + x
BC = 5 + 5
BC = 10.
Read more on triangle midpoint theorem here: brainly.com/question/16047906
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