Question

In the given parallelogram ABCD, find the value of x and y.

Answer 1

ANSWER

Since ABCD is a parallelogram, AB∥DCand AD∥BC


Now, AB∥DC and transversal BDintersects them.


∴∠ABD=∠BDC since alternate angles are equal.


⇒10x=60∘


⇒x=1060∘​=6∘


And, AD∥BC and transversal BDintersects them.


∴∠DBC=∠ADB


⇒4y=28∘


⇒y=428∘​=7

Answer 2

The value of x is 37.33 and y is 35.

Given: Parallelogram ABCD

To Find: x and y

Solution: Since ABCD is a parallelogram, so AD is parallel to BC  (AD ║ BC)

∴ AB is a transversal.

Now, ∠DAB and ∠ABC are consecutive interior angles.

Hence, ∠DAB + ∠ABC = 180°

Putting the values of ∠DAB and ∠ABC:

(3y) + (2y - 5) = 180°

Solving the above equation of angles:

5y - 5 = 180°

5y = 180 - 5 = 175

$y = \frac{175}{5}$

y = 35 (Equation 1)

Now, putting the value of y in ∠DAB

∠DAB = 3y

∠DAB = 3 * 35

∠DAB = 105°

Putting the value of y in ∠ABC

∠ABC = 2y - 5

∠ABC = 2 * 35 - 5

∠ABC = 65°

Similarly, AB is parallel to DC (AB ║ DC)

∴ BC is a transversal.

Now, ∠DCB and ∠ABC are consecutive interior angles.

Hence, ∠DCB + ∠ABC = 180°

Putting the values of ∠DCB and ∠ABC:

(3x + 3) + 65 = 180°

Solving the above equation of angles:

3x + 3 = 180 - 65

3x + 3 = 115

3x = 115 - 3 = 112

$x = \frac{112}{3}$

x = 37.33 (Equation 2)

From equation 1 and equation 2, x = 37.33 and y = 35.

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