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find the value of x in each case:

Q1: 15°

Q2: 37°

Q3: 11°

Step-by-step explanation:

Q1.

CAB = 180 - 8x (straight line)

Similarly, CBA = 180 - 9x

(180 - 8x) + (180 - 9x) + 5x = 180

(Angles in a triangle add to 180)

180 - 8x + 180 - 9x + 5x = 180

360 - 12x = 180

12x = 180

x = 15.

Q2: To find the reflex angle for ABC,

we take 360 - 5x (angles in a point add to 360)

A quadrilateral has 360° in total.

Therefore,

79 + 32 + 2x + (360 - 5x) = 360

79 + 32 + 2x + 360 - 5x = 360

471 + 2x - 5x = 360

471 - 3x = 360

3x = 111

x = 37°

Q3:

BFE = 180 - 147 = 33

FEB = 180 - 4x

x + 33 + 180 - 4x = 180

213 - 3x = 180

3x = 33

x = 11

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

answer: sherk

step-by-step explanation:

just give up and watch the best anime ever sherk