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Question

In the following figure, both ABCD and PQRS are parallelograms. Find the value of x.
1810890_dde102d45e20442fb44af74f1b86347c.png

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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=180B=180120B=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=180x+50+60=180x+110=180
By transposing we get,
x=180110
Therefore, value of x=70

1708926_1810890_ans_812a00b4c1144bf682506b4a0a4a8cf8.PNG

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