Maths-
Explanation :-
- alternate interior angles are supplementary
Therefore, Option A is correct
Maths-General
Explanation :-
- alternate interior angles are supplementary
Therefore, Option A is correct
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 °
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 °
When a transversal cuts two lines such that pairs of alternate interior angles are , then the lines have to be parallel.
Open in App
Suggest Corrections
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
No worries! We‘ve got your back. Try BYJU‘S free classes today!
No worries! We‘ve got your back. Try BYJU‘S free classes today!