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
Lines & Angles
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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.
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