Question

Two adjacent angles of a parallelogram are (3y − 20)˚ and (3y + 80 )˚.

Find the value of y and hence find the measure of each of its angles.​

Answer 1

$\underline\mathfrak{Answer}$

$》(3y − 20)˚ + (3y + 80 )˚ \\ 》 6y + 60 = 180 \\ 》 6y = 180 - 60 \\ 》 6y = 120 \\ 》 y = \frac{120}{6} \\ 》y = 20$

$\underline\mathcal{Y = 20}$

Answer 2

Solution:-

Let us consider a parallelogram ABCD with ∠DAB = (3y - 20)° and ∠ABC = (3y + 80)°.

Now,

We know,

• Sum of the adjacent angles of a parallelogram is 180°.

Therefore,

$\rm : \implies \: \angle \:ABC \: + \: \angle \:DAB \: = \: 180$

$\rm : \implies \:3y + 80 + 3y - 20 = 180$

$\rm : \implies \:6y + 60 = 180$

$\rm : \implies \:6y = 120$

$\boxed{ \pink{ \rm : \implies \:y \: = \: 20}}$

So,

• ∠DAB = (3y - 20)° = (3×20 - 20)° = 40°

and

• ∠ABC = (3y + 80)° = (3×20 + 80)° = 140°

Now,

We know

Opposite angles of a parallelogram are equal.

Therefore,

• ∠DCB = ∠DAB = 40°

and

• ∠ADC = ∠ABC = 140°.

Explore more :-

• A parallelogram is a quadrilateral with two pairs of parallel sides.
• The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. 
• Also, the interior angles on the same side of the transversal are supplementary. 
• Sum of all the interior angles equals 360 degrees.

• Rhombus: If all the sides of a parallelogram are congruent or equal to each other, then it is a rhombus.
• If there is one parallel side and the other two sides are non-parallel, then it is a trapezium.

If ABCD is a parallelogram, where AB || CD and AD || BC. 

• Also, AB = CD and AD = BC
• And, ∠A = ∠C & ∠B = ∠D

Also, ∠A & ∠D are supplementary angles because these interior angles lie on the same side of the transversal.

In the same way, ∠B & ∠C are supplementary angles.

Therefore,

• ∠A + ∠D = 180
• ∠B + ∠C = 180