Question

In the adjoining figure

line l || line m and line n || line P.

Find ∠a, ∠b and ∠c from

the given measure of an angle.​

Answer 1

Step-by-step explanation:

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∘

Answer 2

Answer:

b = 135 ( co exterior angles are supplement )

a= 135 ( vertically opp angles are equal )

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