Question

In the given figure, PQ||RS, angle PAB = 70°, angle ACS = 100°.
Determine angle ABC, BAC and CAQ.​

Answer 1

Answer:

angle ABC = 70°

BAC=30°

CAQ=80°

Step-by-step explanation:

:)

:)

FOR EXPLANATION PLZ REFER TO THE ATTACHMENT MATE!!

have a great day!

Answer 2

Solutions:

Since PQ || RS and transversal AB cuts them at A and B respectively.

Hence, ∠ABC = ∠PAB ............[Alternate angles]

=> ∠ABC = 70° .............. [Since, ∠PAB = 70° (Given)]

Now, PQ || RS and transversal AB cuts them at A and B respectively.

Hence, ∠PAC = ∠ACS .........>>>> [Alternate angles]

=> ∠PAC = 100° ................ [Since, ∠ACS = 100°]

=> ∠PAB + ∠BAC = 100° ............. [Since, ∠PAC = ∠PAB + ∠BAC]

=> 70° + ∠BAC = 100°

=> ∠BAC = 30°

Now, ray AB stands at A on PQ.

Hence, ∠PAC + ∠CAQ = 180°

=> 100° + ∠CAQ = 180°

=> ∠CAQ = 80°

Hence,

∠ABC = 70°,

∠BAC = 30°,

∠CAQ = 80°