Problem 1 : Show Identify the pairs of angles in the diagram. Then make a conjecture about their angle measures. Problem 2 : In the figure given below, let the lines l1 and l2 be parallel and m is transversal. If ∠F = 65°, find the measure of each of the remaining angles. Problem 3 : In the figure given below, let the lines l1 and l2 be parallel and t is transversal. Find the value of x. Problem 4 : In the figure given below, let the lines l1 and l2 be parallel and t is transversal. Find the value of x. Answers1. Answer : Corresponding Angles : ∠CGE and ∠AHG, ∠DGE and ∠BHG, ∠CGH and ∠AHF, ∠DGH and ∠BHF ; congruent. Alternate Interior Angles : ∠CGH and ∠BHG, ∠DGH and ∠AHG ; congruent. Alternate Exterior Angles : ∠CGE and ∠BHF, ∠DGE and ∠AHF ; congruent. Same-Side Interior Angles : ∠CGH and ∠AHG, ∠DGH and ∠BHG ; supplementary. 2. Answer : From the given figure, ∠F and ∠H are vertically opposite angles and they are equal. Then, ∠H = ∠F -------> ∠H = 65° ∠H and ∠D are corresponding angles and they are equal. Then, ∠D = ∠H -------> ∠D = 65° ∠D and ∠B are vertically opposite angles and they are equal. Then, ∠B = ∠D -------> ∠B = 65° ∠F and ∠E are together form a straight angle. Then, we have ∠F + ∠E = 180° Plug ∠F = 65° ∠F + ∠E = 180° 65° + ∠E = 180° ∠E = 115° ∠E and ∠G are vertically opposite angles and they are equal. Then, ∠G = ∠E -------> ∠G = 115° ∠G and ∠C are corresponding angles and they are equal. Then, ∠C = ∠G -------> ∠C = 115° ∠C and ∠A are vertically opposite angles and they are equal. Then, ∠A = ∠C -------> ∠A = 115° Therefore, ∠A = ∠C = ∠E = ∠G = 115° ∠B = ∠D = ∠F = ∠H = 65° 3. Answer : From the given figure, ∠(2x + 20)° and ∠(3x - 10)° are corresponding angles. So, they are equal. Then, we have 2x + 20 = 3x - 10 30 = x So, x = 30° 4. Answer : From the given figure, ∠(3x + 20)° and ∠2x° are consecutive interior angles. So, they are supplementary. Then, we have 3x + 20 + 2x = 180° 5x + 20 = 180° 5x = 160° x = 32° Kindly mail your feedback to We always appreciate your feedback. ©All rights reserved. onlinemath4all.com What are two parallel lines cut by a transversal?If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary . When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles .
When two parallel lines are cut by a transversal What special angles will be formed?When parallel lines are cut by a transversal, there are 4 special types of angles that are formed - corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.
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