Lines Parallel to the same Line

If two lines are parallel with a common line then these two lines will also be parallel to each other.

If AB ∥ CD and EF ∥ CD then AB ∥ EF.

Example

Find x and y.

Solution

\angle A + \angle B + \angle C = 180° (Angle sum property)

30° + 42° + x = 180°

x = 180°- (30° + 42°)

x = 108°

And y is the exterior angle and the two opposite angles are \angle A and \angle B.

So,

\angle BCD = \angle A + \angle B (Exterior angle is equal to the sum of the two interior opposite angles).

y = 30° + 42°

y = 72°

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