what are allied angles? explain it with examples also definition of it.

Allied angles, also known as co-interior angles, are pairs of angles that are formed when two parallel lines are cut by a transversal. These angles are located on the same side of the transversal and inside the parallel lines.

Definition of Allied Angles

In simple terms, allied angles are the angles that lie on the same side of the transversal and between the two parallel lines. The sum of these angles is always equal to 180 degrees.

Examples of Allied Angles

• Example 1: If angle A measures 70 degrees, then its allied angle B, which is on the same side of the transversal, will measure 110 degrees (70 + 110 = 180 degrees).
• Example 2: If angle C is 120 degrees, then the allied angle D will be 60 degrees (120 + 60 = 180 degrees).

Visual Representation

Imagine two parallel lines, line 1 and line 2, with a transversal line crossing them. The angles formed at the intersection points can be labeled. For instance, if angle 1 and angle 2 are on the same side of the transversal and between the two lines, they are allied angles.

Key Points to Remember

• Allied angles are always supplementary, meaning they add up to 180 degrees.
• They are formed when a transversal intersects two parallel lines.

Understanding allied angles is essential in geometry, especially when solving problems related to parallel lines and transversals.