Question

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

Answer 1

Answer :-

• x = 34°
• y = 35°

Given :-

• ∠A = 3y°
• ∠B = (2y - 5)°
• ∠C = (3y - 3)°

To Find :-

• Value of x = ?
• Value of y = ?

Explanation :-

The questioner asks for the values of 'x' and 'y' which are measures of angles in parallelogram ABCD.

Before getting the solution, one needs to be aware of the following properties a parallelogram has :

• Opposite sides are equal.
• Opposite angels are equal.
• Consecutive angles are supplementary.

We need to apply the above mentioned properties to get the solution.

∠A and ∠B are concecutive angles. So, their sum is 180°

∠A = 3y°

∠B = (2y - 5)°

$\rm \mapsto 3y + (2y - 5) = 180^\circ$

$\rm\mapsto 5y - 5 = 180^\circ$

$\rm \mapsto 5y = (180 - 5)^\circ$

$\rm \mapsto 5y = 175^\circ$

$\rm \mapsto y = \sf{\dfrac{175}{5}^\circ}$

$\red{\underline{\boxed{\bf \mapsto y= 35^\circ}}}$

Measure of y = 35°

Measure of ∠A

$\rm \mapsto \angle A = 3(35)^\circ$

$\rm \mapsto \angle A = 105^\circ$

∠A and ∠C are opposite angles. So, their measure will be same.

∠C = 105°

$\rm \mapsto 3x + 3 = 105^\circ$

$\rm \mapsto 3x = (105 - 3)^\circ$

$\rm \mapsto 3x = 102^\circ$

$\rm\mapsto x = {\dfrac{102}{3}^\circ}$

$\red{\underline{\boxed{\bf \mapsto x = 34^\circ }}}$

Measure of x = 34°

Therefore, the measure of x and y is 34° and 35° respectively.