Question

some parallelogram are given below find X and Y?

Answer 1

So, The value of $X\ and\ Y$ in figure(a) is $70\ degree\ and\ 110\ degree$ ,the value of $X\ and\ Y$ in figure(b) is $10\ units\ and\ 3\ units$ and the value of  $X\ and\ Y$ in figure(c) is $70\ degree\ and\ 110\ degree$.

Step-by-step explanation:

Given,

Find the value $X\ and\ Y$ from figure.?

Figure(a):

In any parallelogram,

Opposite angles are congruent.

So,

$\angle A=\angle C\ and\ \angle B=\angle D$

∴ $\angle D=Y=110\ degree$ (∵ $\angle B=110\ degree$ )

So,

$2\angle A+2\angle B=360$

⇒$2X=360-(2\times 110)$

⇒$2X=140$

⇒$X=70\ degree$

So, The value of $X\ and\ Y$ in figure(a) is $70\ degree\ and\ 110\ degree$

Figure(b):

We know,

The diagonals of a parallelogram bisect each other.

So,

$2X-5=15$

⇒$2X=15+5=20$

⇒$X=10$

And,

$Y+7=10$

⇒$Y=10-7=3$

The value of $X\ and\ Y$ in figure(b) is $10\ units\ and\ 3\ units$

Figure(c):

$UV\parallel TW$ and $TS$ is the intersecting line.

So, Corresponding angles are equals.

∴ $\angle UTW=\angle SUV=X=75\ degree$

So, $\angle TUV=180-\angle SUV$

⇒$\angle TUV=180-75$

⇒$\angle TUV=105\ degree$

In parallelogram $TUVW$,

$\angle TWV=\angle TUV$

⇒$Y=105\ degree$

The value of  $X\ and\ Y$ in figure(c) is $70\ degree\ and\ 110\ degree$

Answer 2

Answer:

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