Question

in figure line l || line m and line n || line p find angle a and angle C​

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=45  

∘

Step-by-step explanation: