Question

Find the value of X and Y in the given parallelogram.

Answer 1

Answer:

THE OPPOSITE ANGLES OF A PARALLELOGRAM ARE EQUAL

6y = 120°

y = 120° / 6

y = 20°

ADJACENT ANGLES IN A PARALLELOGRAM ARE 180°

5x + 10° + 120° = 180°

5x + 130° = 180°

5x = 180° — 130°

5x = 150°

x = 150° / 5

x = 30°

Step-by-step explanation:

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Answer 2

We Know,

$\text{Sum of adjacent angles of a ||gm is 180°.}$

$= \bf = > 5x + 10 + 6y = 180 \degree \\ \bf = > \: \: \: \: \: \: \: \: 5x + 6y = (180 - 10) \degree \\ \bf = > \: \: \: \: \: \: \: \: 5x + 6y = 170\degree \: \: \: \: \: \: .... \: (a)$

Also,

$\text{The Opposite angles of a ||gm are equal.}$

$\bf.°. \: \: \: \: \: \: \: 6y = 120 \\ \sf \: \: \: \: \: \: \: = > y = \frac{120}{6} = \frac{ \cancel6 \times 20}{ \cancel6} \\ \sf \: \: \: \: \: \: \: = > y = 20$

Now,

Putting y in equation (a), we get,

$\sf{5x + 6y = 170} \\ \sf5x + 6(20) = 170 \\ \sf = > \: \: \: \: \: \: 5x = 170 - 120 \\ \sf = > \: \: \: \: \: x = \frac{170 - 120}{5} \\ \\ \sf = > \: \: \: \: \: \: x = \frac{50}{2} \: \: \: = 25$

Hence,

$\boxed{ \boxed{ \bf \huge x = \red2 \red5 }}\\ \boxed{ \boxed{ \bf \huge y = \red2\red0}}$