Question

in the fig AB||CD and a transversal line pq cuts them.if 1=65°,find all other angles
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Answer 1

Answer:

Step-by-step explanation:

Answer 2

The measurements are ∠2 = 115°,  ∠3 = 115°, ∠4 = 115°, ∠5 = 115°, ∠6 = 115°,  ∠7 = 115°  and ∠8 = 65°

Given:

In the fig AB||CD and a transversal line pq cuts them.if ∠1=65°

To find:

All remaining angles in given picture

Solution:

Given that ∠1 = 65°

From line AB

⇒ ∠5 + ∠1 = 180°

⇒ ∠5 + 65° = 180°

⇒ ∠5 = 115° __(1)

Here, ∠1 = ∠8  [ ∵∠1 and ∠8 are corresponding angles ]

⇒ ∠8 = 65°

∠5 = ∠7   [ ∵ ∠5 and ∠7 are corresponding angles ]  

⇒ ∠7 = 115°    

From line PQ

⇒ ∠1 +∠6 = 180°

⇒  65° + ∠6 = 180°

⇒ ∠6 = 115°  

Here,  ∠6 = ∠4   [ ∵ ∠6 and ∠4  are corresponding angles ]

⇒ ∠4 = 115°

From line PQ

∠5 + ∠2 = 180°

∠2 = 180°- 65°

∠2 = 115°

∠2 = ∠3  [ ∵ ∠2 = ∠3  are corresponding angles ]

⇒ ∠3 = 115°

Therefore, the measurements are

∠2 = 115°,  ∠3 = 115°, ∠4 = 115°, ∠5 = 115°, ∠6 = 115°,  ∠7 = 115°  and ∠8 = 65°  

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