what are allied angles

if two parallel lines are cut by a transversal as shown in above diagram.

then x and u are allied angles and v and z are allied angles.

allied angles are also called as co-interior angles.

hope this helps you.


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Allied angle is an angle pair, which is created by transversal line . Now question arises what are allied angles? We assume a transversal line GH, which intersect two straight lines PQ and RS and create 8 angles on both Straight Line PQ and RS: 
4 angles on PQ: angle p, angle q, and angle r and angle s, 
4 angles on RS: angle t, angle u, angle v and angle w, 
Here angle‘s’ and angle ‘u’, angle ‘r’ and angle‘t’ are allied angles because these angles are adjacent from different straight line with each other. Now question arises how we calculate allied angles: 
We use following steps for finding an allied angle– 
Step 1: Initially we calculate one angle from two allied angles like angle ‘s’ and angle ‘u’ are allied angles and value of angle ‘s’ is equal to 70 degree and value of angle ‘u’ is equal to ‘x + 40’ degree. 
Step 2: After evaluation of one allied angle, now we apply following formula for calculation of other allied angle– 
Angle s + angle u = 180, 
= > 70 + (x + 40) = 180, 
= > x + 110 = 180, 
= > x = 180 – 110 = 70 degree 
So, other allied angle from two allied angles is equal to (70 + 40 = 110) degree, whose first allied angle is equal to 70 degree.

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You may know them as Interior or even co-interior angles.

Draw a pair of parallel lines, and then a line crossing through them.

The allied angles are the ones "inside" and they add up to 180 degrees.




Now we take an example to understand the process of evaluating allied angles:
Example: Find allied angle, whose one allied angle is equal to 55 degree?
Solution: we use following formula for evaluation of allied angle -
Angle 1 + angle 2 = 180 degree,
= >55 + angle 2 = 180,
= > angle 2 = 180 – 55 = 135 degree,
So, other allied angle is equal to 135 degree.

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