Question

7. In the given figure, P is a point in the interior of
ZAOB. PM I OB and PN 1 OA.
If ZNOM = 60°, what is the measure of ZNPM?
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Answer 1

Since AB || CD and BC is a transversal.

So, ∠ABC = ∠BCD                [atternate interior angles]

⇒ 70o = xo + ∠ECD ….(i)

Now, CD || EF and CE is transversal.

So, ∠ECD + ∠CEF = 180o     [sum of consecutive interior angles is 180o]

∴ ∠ECD + 130o = 180o

⇒ ∠ECD = 180o – 130o = 50o

Putting ∠ECD = 50o in (i) we get,

70o = xo + 50o

⇒ x = 70 – 50 = 20