Question

In the figure line L // line M & line PQ is the transversal if angle PEB = 70 ° and find the measures of each of the remaining angles

please give step by step and correct answer ​

Answer 1

Answer:

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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=45∘

Step-by-step explanation: