Problem 1 : 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'. 1. Answer :
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° Substitute ∠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 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 parallel lines cut by a transversal?If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.
What angle relationships are created when parallel lines are intersected by a transversal?When a transversal line crosses a pair of parallel lines, you'll find many pairs of supplementary angles, or angles that add to 180 degrees. Angles directly opposite each other, called vertical angles, are congruent.
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