Construct a quadrilateral $A B N V$ where $A V = 7 c m, B A = 8 c m, B N = 10 c m, N V = 5 c m$ and $B V = 11 c m .$ Then, the measure of $∠ N B V$ (in deg.) is ?

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Solution

1. Draw a line segment $B V = 11 c m$ .
2. With $10 c m$ as radius, draw an arc from $B$ .
3. Similarly, with radius as $5$ cm from $V$ , cut the arc just drawn.
4. They will intersect at $N$ . Join $B N$ and $V N$ .
5. With $7 c m$ as radius, draw an arc from $V$ . Similarly, with radius as $8 c m$ from $B$ , cut the arc just drawn.
6. They will intersect at $A$ . Join $A B$ and $V A$ .
7. $A B N V$ is the required quadrilateral.
8. Using Protractor, we can measure $∠ N B V$ which comes out to be $30 ˚$ .

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A B N V

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B V = 11 c m .

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V B = 11 c m .

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