Answer:
They are two angles that have a common vertex and a common side.
Step-by-step explanation:
Let`s assume that points M, N and P are the touching points of those 3 circles:Then:Y M + M Z = 14,Z N + N X = 20X P + P Y = 18And also: M Z = ZN, Y M = P Y and N X = X P.Now we have a system of 3 equations ( Y M, M Z and X P are the radii of each circle ):Y M + M Z = 14M Z + X P = 20X P + Y M = 18 Y M - M Z = - 14+X P + Y M = 18 X P - M Z = 4Y M - M Z = - 14+M Z + X P = 20 X P - Y M = 6 /* ( - 1 )X P - M Z = 4 X P + Y M = - 6 X P - M Z = 4 Y M - M Z = - 2 Y M + M Z = 14 2 Y M = 12 => Y M = 6M Z - 6 = 2 => M Z = 8X P + 6 = 18
X P = 12
Radii of the circles are: 12, 8 and 6.
Answer:
Parallel line:
Perpendicular line:
Step-by-step explanation:
we are given equation 4x+5y=19
Firstly, we will solve for y
we can change it into y=mx+b form
so,
Parallel line:
we know that slope of two parallel lines are always same
so,
Let's assume parallel line passes through (1,1)
now, we can find equation of line
we can plug values
now, we can solve for y
Perpendicular line:
we know that slope of perpendicular line is -1/m
so, we get slope as
Let's assume perpendicular line passes through (2,2)
now, we can find equation of line
we can plug values
now, we can solve for y
The answer would be <QRZ
Since you are looking for an angle congruent to <UQR using the alternate interior angles theorem, interior suggests that the angle must be inside the parallel lines, se we can get rid of options <WRT and <TRZ since they are exterior angles
Furthermore, in the alternate interior angles theorem, the two angles must be alternate or opposite of each other which would show that the only possible answer would be <QRZ
hope this helped!
I think it’s b but don’t take my word for it
