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:
129 = x
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
47+82 = x
129 = x
Answer:
x = 80
Step-by-step explanation:
Thank you for the clear diagram. We don't always get them.
Argument
There are two kinds of angles associated with a triangle
- Interior angles
- Exterior angles
You have both kinds in this question. The interior angles are the ones that make up the triangle itself. The ones you are concerned about are x and 38°.
The other kind is formed by extending one of the sides. In this question, the value of the exterior angle is 118°.
Rule
The two interior angles NOT connected to the given exterior angle are equal (when added) to the exterior angle.
In plain English what that means is
x + 38 = 118
Solution
x + 38 = 118 Subtract 38 from both sides.
x + 38 - 38 = 118 - 38
x = 80
So x = 80
5/6 is greater than 2/3
Multiply both numerator & denominator by 2 in order to have common denominators, 2/3 * 2/2 = 4/6
Now, you can see, 5 is greater than 4, in the numerator so 5/6 would be greater
Hope this helps!
