Question

In the given figure, line l || line m and line n || line p.

Find, ∠a, ∠b, ∠c from the given measure of an angle.

Answer 1

Let us mark the points R and S on line n, T and U on line p, A and B on line l and C and D on line m.

Suppose the lines n and p intersect the line l at K and L respectively and line m at M and N respectively.

Since, the line l and line p intersect at L, then

∠KLN = ∠BLT    ...(Vertically opposite angles)

⇒ ∠KLN = 45^∘

Since, line l || line m and line p is a transversal intersecting them at L and N, then

∠KLN + ∠MNL = 180^∘    ...(Pair of interior angles on the same side of transversal is supplementary)

⇒ 45^∘ + ∠a = 180^∘

⇒ ∠a = 180^∘ − 45^∘ 

⇒ ∠a = 135^∘

Since, the line m and line p intersect at N, then

∠DNU = ∠MNL    ...(Vertically opposite angles)

⇒ ∠b = ∠a = 135^∘

Since, line n || line p and line m is a transversal intersecting them at M and N, then

∠NMS = ∠DNU    ...(Corresponding angles)

⇒ ∠c = ∠b = 135^∘