if AB//cd, angle QPR = 60° and angle 125° then find the angles x, y and z
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✬ ∠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}
∠PQR + 125° = 180°
∠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°.
∠y + ∠x + ∠z = 180°
60° + ∠x + 55° = 180°
115° + ∠x = 180°
∠x = 180° – 115°
∠x = 65°
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