In the following figure, both ABCD and PQRS are parallelograms. Find the value of x.
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Solution
From the figure, it is given that, ABCD and PQRS are two parallelograms. ∠A=120∘ and ∠R=50∘ We know that, ∠A+∠B=180∘ 120∘+∠B=180∘∠B=180∘−120∘∠B=60∘ In parallelogram opposite angles are equal.
⇒∠P=50o
Then, consider the triangle MPB we know that the sum of measures of interior angles of the triangle is equal to 180∘. ∠PMB+∠P+∠B=180∘x+50∘+60∘=180∘x+110∘=180∘ By transposing we get, x=180∘−110∘ Therefore, value of x=70∘