Question

In the given figure line r ∥ line s and line t ∥ line u. Find the measure of ∠a, ∠b and ∠c from the information provided.​

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

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

∠KLN+∠MNL=180

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(Pair of interior angles on the same side of transversal is supplementary)

⇒45

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+∠a=180

∘

⇒∠a=180

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−45

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=135

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

∠DNU=∠MNL (Vertically opposite angles)

⇒∠b=∠a=135

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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

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