Mathematics
Two lines AB and CD are cut by a transversal EF, as shown in the figure. Identify the given pair of angles as adjacent angles, vertically opposite angles, alternate angles, corresponding angles or co-interior angles.
(i) ∠6 and ∠7
(ii) ∠3 and ∠4
(iii) ∠4 and ∠8
(iv) ∠1 and ∠5
(v) ∠3 and ∠5
(vi) ∠2 and ∠4
(vii) ∠4 and ∠5
(viii) ∠2 and ∠7
(ix) ∠3 and ∠6
(x) ∠4 and ∠6
(xi) ∠2 and ∠6
(xii) ∠1 and ∠4
Answer
(i) ∠6 and ∠7
These angles are opposite each other at the same intersection point formed by two intersecting lines CD and EF.
∴ These are vertically opposite angles.
(ii) ∠3 and ∠4
These angles share a common vertex and a common arm on line AB, and lie next to each other without overlapping.
∴ These are adjacent angles.
(iii) ∠4 and ∠8
These angles are in the same relative position (bottom-right) at each intersection.
∴ These are corresponding angles.
(iv) ∠1 and ∠5
These angles are in the "top-left" position at each intersection.
∴ These are corresponding angles.
(v) ∠3 and ∠5
These angles lie inside the two parallel lines and are on the same side of the transversal.
∴ These are co-interior angles.
(vi) ∠2 and ∠4
These angles share a common vertex and a common arm and lie next to each other without overlapping.
∴ These are adjacent angles.
(vii) ∠4 and ∠5
These angles lie between the two parallel lines but on opposite sides of the transversal.
∴ These are interior alternate angles.
(viii) ∠2 and ∠7
These angles lie outside the two parallel lines and on opposite sides of the transversal.
∴ These are exterior alternate angles.
(ix) ∠3 and ∠6
These angles lie between the two parallel lines but on opposite sides of the transversal.
∴ These are interior alternate angles.
(x) ∠4 and ∠6
These angles lie inside the two parallel lines and on the same side of the transversal.
∴ These are co-interior angles.
(xi) ∠2 and ∠6
These angles are in the same relative position (top-right) at different intersections.
∴ These are corresponding angles.
(xii) ∠1 and ∠4
These angles are opposite each other at the same intersection point formed by two intersecting lines AB and EF.
∴ These are vertically opposite angles.
Related Questions
In the given figure, two lines AB and CD intersect at a point O. If ∠AOC + ∠BOD = 70°, find the measure of ∠AOD.
In the given figure, the lines AB, CD and EF intersect at a point O. If ∠BOD = x°, ∠AOE = 2x° and ∠COF = 90°, find ∠AOE and ∠AOC.
In the given figure, AB || CD and EF is a transversal. If ∠8 = 110°, find each one of the unknown angles, marked in the figure. Give reasons.
In each of the following figures, AB || CD and EF is a transversal. Find each one of the unknown angles x, y, z in each case.
(i)
(ii)
(iii)
