(69 ! answer ! , will mark as brainliest if u give an explantion and not like just the answer =.= ) △abc has interior angles with measures x°, 90°, and 65°, and △def has interior angles with measures y°, 65°, and 20°. using the given information, which statement is true? the two triangles are similar because y=90 . the two triangles are not similar because the interior angles are congruent but the side lengths are different. the triangles are similar because they each have an interior angle with measure 65°. the two triangles are not similar because x≠20 and there cannot be three congruent interior angels.

Okay so process of elimination. The first option isn't correct because the sum of the interior angles for any triangle is always 180 degrees. x would be 25 degrees  for ABC because 90+65=155 and 180-155=25. Y would be 95 degrees for DEF because 65+20=85 and 180-85=95, so y does not equal 90 degrees. For B, No side lengths are given. C is also not the correct answer so the answer is D. I can link you to another post that has the same question or a similar with an explanation on determining the answer if you'd like :)

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

answer: 40.95

step-by-step explanation: