I could not figure this out if my life depended on it. I have over 40 of these questions and I'm so confused. Please help and show work because I really need to understand this.
I'll try a few
In the first one.....these chords have the same length....so....this implies that
(7x - 39)° = 87°
7x - 39 = 87 add 39 to both sides
7x = 126 divide both sides by 7
x = 18
Second one.....same thing.....the chords LM and NP have the same length
So
41 - 2x = 7x + 5 add 2x to both sides.....subtract 5 from both sides
36 = 9x divide both sides by 9
4 = x
So
LM = 41 - 2x = 41 - 2(4) = 41 - 8 = 33
Third one
Since chords DE = GF....equal chords are the came distance from the center of the circle
This implies that HJ = JI ....so....
3x + 20 = 15x - 64 add 64 to both sides, subtract 3x from both sides
12x = 84 divide both sides by 12
x = 7
So JI = 15x - 64 = 15(7) - 64 = 105 - 64 = 41
Fourth one
LM and NP are equal distances from the center of the circle....so....they have equal length
Then.....they also span the same arcs
This implies that
(8x - 56)° = (5x + 22)°
8x - 56 = 5x + 22 add 56 to both sides, subtract 5x from both sides
3x = 78 divide both sides by 3
x = 26
So LM spans an arc of 8(26) - 56 = 208 - 56 = 152°
And NP spans the same arc
So LP spans an arc = 360 - LM - NP - MN =
(360 - 152 -152 - 39)° = 17°
Last one
Equal segments drawn from the center of the circle meet chords BC and CD at right angles
This means that the two chords are equal and thus, they span the same arcs....so....like before...
9x - 53 = 2x + 45 add 53 to both sides and subtract 2x form both sides
7x = 98 divide both sides by 7
x = 14
So each chord spans an arc of 9(14) - 53 = 73°
Then BAD will span an arc = 360 - 73 - 73 = 214°