I've tried to solve these but I don't understand it at all. Please show how to solve this because I'm not good at these types of questions and I need to understand this. Thank you.
First one.....
Note that central angle CHD is right = 90°
And the measure of arc CD has the same measure = 90°
Angle DHE also = 90° [ since it is supplemental to angle CHD]
So arc DE has the same measure = 90°
And arc FE = 34°
So...arc FD [I'm asssuming arc FED ] is the sum of these two arcs = 124°
The measure of arc DCF = 360 - measure of arc FD = 360 - 124 = 236°
The measure of arc GDF = measure of arc GCD + measure of arc FED = 180 + 124 = 304°
Second one [ at the top right ]
Notice that angle QUR is a vertical angle to angle TUS.....so its measure is also = 19°
And the measure of angle PUR = 90°
So the measure of arc PQ = measure of angle PUQ = measure of angle PUR - measure of angle QUR =
90 - 19 = 71°
Measure of arc SR = 180 - 19 = 161°
Measure of arc QRT = measure of arcs SR + QR = 180 + 19 = 199°
Measure of arc PSR = measure of arc PT + measure of arc TSR = 90 + 180 = 270°
Measure of arc PS = measure of arc PT + measur of arc TS = 90 + 19 = 109°
Third one
Note that arc JK + arc KL =180
Therefore
(5x + 23) + (17x - 41) = 180 simplify
22x - 18 = 180 add 18 to both sides
22x = 198 divide both sides by 22
x = 9
arc JK = 5x + 23 = 5(9) + 23 = 45 + 23 = 78°
Since angle MVJ = angle LVK, arc MJ = arc KL = 17x - 41 = 17(9) - 41 = 112°
arc LMK = arc LMJ + arc JK = 180 + 78 = 258°
Last one
Note that the sum of arcs YX, XW and WV = 360 - arc VY = 360 - 90 = 270°
So we have this
(10x + 9) + ( 21x - 12) + ( 8x) = 270 simplify
39x - 3 = 270 add 3 to both sides
39x = 273 divide both sides by 39
x = 7
arc WX = 21x - 12 = 21(7) - 12 = 148 - 12 = 136°
arc YW = hard to tell which arc is being referred to, here arc YVW or arc YXW ???
arc YX = 10x + 9 = 10(7) + 9 = 70 + 9 = 79°
arc VXW = 360 - arc VW = 360 - 8x = 360 - 8(7) = 360 - 56 = 204°