Question

In the figure below if line ab parallel to line CD parallel to line PO then find the value of x

Answer 1

We know that the angles on the same side of the transversal is equal to 180°.

So, ∠PQR+∠QRX = 180°

Or, ∠QRX = 180°-110°

∴ ∠QRX = 70°

Similarly,

∠RST +∠SRY = 180°

Or, ∠SRY = 180°- 130°

∴ ∠SRY = 50°

Now, for the linear pairs on the line XY-

∠QRX+∠QRS+∠SRY = 180°

Putting their respective values, we get

∠QRS = 180° – 70° – 50°

Hence, ∠QRS = 60°

Answer 2

i think x is 40°

if line CD is parallel to PO, angle DCE and angle CEO are supplementary, meaning angle CEO is equal to 80°. we also know if line AB is parallel to line PO, angle ABE and angle BED are congruent. angle BED = x + angle CEO.

substitute our known values:
120=x+80
x=40°