Parallel Lines and Transversal Application Question 1

Here is our problem. In the figure here, AB is parall to CD. is the transversal intersecting AB at point and CD at point This angle that means angle is 80°. This angle is 2X - and this angle is + We have to find the value of here. For finding the value of here, we will have to form equations and choose the best way for finding the value of By solving this problem, we aim to learn how to apply relevant properties of parallel lines for solving problem. Also we aim to learn the relevance of algebraic equations. Here in this question angle that means this angle and angle OPD that means this angle are corresponding angles and we know that corresponding angles are equal. So we can have here + is equal to 80° we can call this as 1. Reason is corresponding angle exom. Also angle that means this angle and angle od that means this angle are consecutive interior angles. So that would mean that sum of these angles that is 2x - + + is equal to 180° we can call this as 2. So the reason we have written here co-int angles are supplementary also this angle that means angle and this angle that means angle form linear pair. So we can have one equation from here also that is 2x - + 80° that is is equal to 180°. We can call this as three. Reason is linear pair. In this question, if we had to find angle and angle OPD, then it would have been easier. But here we need to find the value of So we have three equations here and out of these three equations which equation do you think we should use in order to get the answer in easiest possible way. So if we look at equation two here we can cancel minus and + and then we will have 3x = 180° very easily we can find the value of and once we find the value of we can put the value of in equation one to find the value of So by making use of equation two we have the easiest way of finding the variable Using equation 2 we have 2x - + + is = 180°. - cancels with + This implies we have 3x is equal to 180°. This implies is equal to 180° by 3 that is equal to 60°. Put is equal to 60° in equation 1. We will have 60° + is equal to 80°. This implies is equal to 80° - 60° is equal to 20°. So this is the value of which we had to find in the question. Let's summarize what we have learned in this question. We learned how to choose the right pair of angles and apply their properties. We also learned how to form equations and solve the problem.