Question

find x and y in the following figures

Answer 1

Ok so first we find angle PAB
Since BAD=100, PAB=80.
So the angle PBA=180-120=60.
If PBA=60, then PCD is also 60.
So x=60.
Now we find y.
y=180-160=20.
If I made any mistakes, please tell me

Answer 2

Hey there!

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Question: Find values of 'x' and 'y'

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Answer

Given,

ABCD is a trapezium

∠BAD = 100°

∠PAB = 40°

AB║CD since ABCD is a trapezium.

To find,

∠x and ∠y

Solution,

Consider Trapezium ABCD

AB║DC  and AD is the transversal,

∴ ∠y=∠BAD (co-interior angles)

  ∠y = 100° (∠BAD = 100°)

Now, considering Δ PDC

∠P + ∠D + ∠C = 180°  (ASP of a triangle)

40° + y + x = 180°

40° + 100 + x = 180°

        140° + x = 180°

                   x = 180° - 140°

                  ∴ x = 40°

Therefore, now we have the values that

x = 40 and y = 100

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TIP: If you're unsure with the result, you can always add the three angles of the triangle and you must obtain 180° as the sum if your answer is correct. If you dont, do recheck the answer. Lets apply this technique now

= x + y + P

= 40 + 100 + 40

= 180°

Therefore the obtained angles are correct!

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Hope it helps!