Math, asked by xoxo777, 9 months ago

if AB//cd, angle QPR = 60° and angle 125° then find the angles x, y and z​

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Answered by pandaXop
22

∠y = 60° , z = 55°

x = 65°

Given:

  • Line AB is parallel to line CD
  • ∠QPR is 60°.
  • ∠BQR is 125°.

To Find:

  • What are the measures of angle x , y and z?

Solution: Since, AB || CD therefore,

➱ ∠QPR = ∠PRC or ∠y {Alternate interior angles}

➱ 60° = ∠y

So, The measure of ∠y is 60°.

➱ ∠PQR + ∠BQZ = 180° {Linear pair angles}

\implies{\rm } ∠PQR + 125° = 180°

\implies{\rm } ∠PQR = 180° – 125 = 55°

Also,

➱ ∠PQR = ∠QRD or ∠z {Alternate interior angles}

➱ 55° = ∠z

So, The measure of ∠z is 55°.

Now, We can see that ∠y , ∠x and ∠z are in straight line therefore their sum should be 180°.

\implies{\rm } ∠y + x + z = 180°

\implies{\rm } 60° + x + 55° = 180°

\implies{\rm } 115° + x = 180°

\implies{\rm } x = 180° 115°

\implies{\rm } x = 65°

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