Question

if the arms of one angle are respectively parallel to the arms of other angle, prove that the two angles are either equal or supplementary​

Answer 1

Answer:

Let’s consider that arms, of angle ABC and angle PQR, AB//PQ & BC//QR.

Case 1:

Considering figure 1,

∠ABC = ∠PSC … [corresponding angles]

Also, ∠PSC = ∠PQR… [corresponding angles]

∴ ∠ABC = ∠PQR …. (i)

Case 2:

Considering figure 2,

Extending line QR to T intersecting AB at S.

∠ABC = ∠AST….. [corresponding angles]

Also, ∠AST = 180° - ∠ASR …. [Linear pair]

∴ ∠ABC = 180° - ∠ASR …. (ii)

Now, ∠ASR = ∠PQR …. (iii) [corresponding angle]

From (ii) & (iii), we get

∠ABC = 180° - ∠PQR

∴ ∠ABC + ∠PQR = 180° …… (iv)

Thus, from (i) & (iv), we can say that

If the arms of one angle are respectively parallel to the arms of other angle, then the two angles are either equal or supplementary to each other.

Hence proved.

Answer 2

Step-by-step explanation:

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