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What are Allied Angles?

TopAllied 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.

Trigonometric Ratios of Allied Angles

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.