I'm assuming D is the center of the circle. See the new figure.
Angle BDC = 106 degrees, that's the definition of arc measure.
Triangle BDC is isosceles (two radii make congruent sides) so the two remaining angles in BDC are equal, DBC=DCB=(180-106)/2=37 degrees.
Angle BAC = 106/2 = 53 degrees, subtending the arc of 106 degrees.
Angle CAD = 53/2 = 26.5 degrees because AD is a bisector, the shared hypotenuse of congruent right triangles AED and AFD.
AFD is also congruent to CFD, so angle DCA is also 26.5 degrees
Angle ACB is the sum of DCA and DCB, ACB = 26.5 + 37 = 63.5 degrees
The angle subtends the arc we seek, whose measure must be double:
10x - 23 = 2(63.5) = 127 degrees
10x = 150
x = 15
Answer: 15
558 gallons are used when the car has been driven 18 miles.
<u>Step-by-step explanation:</u>
<u>From the given data, it can be determined that :</u>
- The number of gallons for 2 miles = 62 gallons
- The number of gallons for 4 miles = 124 gallons
- The number of gallons for 10 miles = 310 gallons
Let, the number of gallons for 18 miles = 'x' gallons
<u>To find x :</u>
compare the given data with the unknown data,
62 gallons / 2 miles = x gallons / 18 miles
keep x alone on one side,
x = (62×18) / 2
x = 31×18
x = 558 gallons
Therefore, 558 gallons are used to drive 18 miles.
I don't know if I'm right the answer could be 6x