Question

4.
In each of the following parallelograms find the measure of x, y, z.
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Answer 1

We know that adjacent angles of a parallelogram ABCD are supplementary.

∴∠A+z=180∘

⇒z=180∘−120∘=60∘

We We know that opposite angles of a parallelogram ABCD are equal.

∴z=∠CDA=60∘ and ∠BAD=∠BCD=120∘

∠B=z+a=180∘(linear pair)

⇒a=180∘−z=180∘−60∘=120∘

⇒x+∠DCB=180∘(linear pair)

⇒x=180∘−∠DCB=180∘−120∘=60∘

⇒y+∠CDA=180∘(linear pair)

⇒y=180∘−∠CDA=180∘−60∘=120∘

∴a=120∘,z=60∘,x=60∘,y=120∘