Maths- Explanation :-As we know corresponding angles are equal thenwe get ∠1 =∠3 , ∠2 =∠4, x =∠5 and ∠6=∠8As we know vertically opposite angles are equalwe get ∠1 = x , ∠2=∠8, ∠3 =∠5 and ∠4 =∠6From above equations we get ∠1 =∠3 = ∠5 = x = 60 °and ∠2 =∠4 =∠6 =∠8As we know, the sum of angles in a straight line is 180° . We get∠2+x = 180 then ∠2 = 180 °-x∠2 = 180 °- 60 °∠2 = 120 ° Therefore we get ∠2 =∠4 =∠6 =∠8 = 120 ° and ∠1 =∠3 = ∠5 = 60 ° Maths-General Explanation :-As we know corresponding angles are equal thenwe get ∠1 =∠3 , ∠2 =∠4, x =∠5 and ∠6=∠8As we know vertically opposite angles are equalwe get ∠1 = x , ∠2=∠8, ∠3 =∠5 and ∠4 =∠6From above equations we get ∠1 =∠3 = ∠5 = x = 60 °and ∠2 =∠4 =∠6 =∠8As we know, the sum of angles in a straight line is 180° . We get∠2+x = 180 then ∠2 = 180 °-x∠2 = 180 °- 60 °∠2 = 120 ° Therefore we get ∠2 =∠4 =∠6 =∠8 = 120 ° and ∠1 =∠3 = ∠5 = 60 ° Open in App Suggest Corrections 1
In geometry, a transversal is a line that intersects two or more other (often parallel ) lines. In the figure below, line n is a transversal cutting lines l and m .
When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles . In the figure the pairs of corresponding angles are: ∠ 1 and ∠ 5 ∠ 2 and ∠ 6 ∠ 3 and ∠ 7 ∠ 4 and ∠ 8 When the lines are parallel, the corresponding angles are congruent . When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles . In the above figure, the consecutive interior angles are: ∠ 3 and ∠ 6 ∠ 4 and ∠ 5 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 . In the above figure, the alternate interior angles are: ∠ 3 and ∠ 5 ∠ 4 and ∠ 6 If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent . When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles . In the above figure, the alternate exterior angles are: ∠ 2 and ∠ 8 ∠ 1 and ∠ 7 If two parallel lines are cut by a transversal, then the alternate exterior angles formed are congruent .
Example 1:
In the above diagram, the lines j and k are cut by the transversal l . The angles ∠ c and ∠ e are… A. Corresponding Angles B. Consecutive Interior Angles C. Alternate Interior Angles D. Alternate Exterior Angles The angles ∠ c and ∠ e lie on either side of the transversal l and inside the two lines j and k . Therefore, they are alternate interior angles. The correct choice is C .
Example 2:
In the above figure if lines A B ↔ and C D ↔ are parallel and m ∠ A X F = 140 ° then what is the measure of ∠ C Y E ? The angles ∠ A X F and ∠ C Y E lie on one side of the transversal E F ↔ and inside the two lines A B ↔ and C D ↔ . So, they are consecutive interior angles. Since the lines A B ↔ and C D ↔ are parallel, by the consecutive interior angles theorem , ∠ A X F and ∠ C Y E are supplementary. That is, m ∠ A X F + m ∠ C Y E = 180 ° . But, m ∠ A X F = 140 ° . Substitute and solve. 140 ° + m ∠ C Y E = 180 ° 140 ° + m ∠ C Y E − 140 ° = 180 ° − 140 ° m ∠ C Y E = 40 ° |