Question

10 cr

7. If the quadrilateral ABCD is a parallelogram, what
the value of x?
(3x + 3) + 3y (2y-5)
(i) 45°
(ii) 30°
(iii) 36°
(iv) 37°
3yº

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Answer 1

Answer:

(3)

In parallelogram ABCD,

We know that the opposite angles of a parallelogram are equal.

Hence ∠A=∠C

⇒3y=3x+3 ...(1)

and ∠B=∠D

∴ ∠D=2y−5 ...(2)

We know that the sum of angles of a parallelogram is 360°

⇒(3y)+(3x+3)+(2y−5)+(2y−5)=360

⇒3y+3y+4y−10=360

⇒10y−10=360

⇒10y=360+10

⇒10y=370

y= 37°

Substitute y=37° in (1)

⇒3×(37°)=3x+3

⇒111=3x+3

⇒3x=111−3

⇒3x=108

⇒x= 108/3

x=36°