Question

in the given figure,line p || line m || line n. Find angle x.
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Answer 1

Answer:

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

∘

=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

∘

solution

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Answer 2

Answer:

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

∘

=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

∘

Step-by-step explanation:

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