Solve for xan explanation would be great.

When two lines intersect, (in this case it's a ray and a line), they form a linear pair. Here, we know that because those two angles form a linear pair. Solving for x we have :

The angle is a straight angle. Straight angles measure 180°. One of the angles measures 93°. Subtract 93 from 180.

That means:

Switch it around and it becomes:

The sign changes when you move it to the other side. at first you were adding, and now you're subtracting.

Subtract:

Divide both sides by 3 to leave the variable alone:

That means x = 23

  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.

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation: