Question

the adjacent angle of a parallelogran are (3x-12)° and (52+x)°. find the angle of the The parallelorgan.​

Answer 1

Given :-

• Adjacent angles of a parallelogram are

= ( 3x - 12)° and ( 52 + x) °

Solution :-

[ It is a parallelogram and we know that the interior angles on the same side of a transversal are supplementary ]

Here,

Two adjacent angles of parallelogram are

( 3x - 12)° and ( 52 + x) °

Therefore,

( 3x - 12)° + ( 52 + x) ° = 180°

3x - 12 + 52 + x = 180°

4x + 40 = 180°

4x = 180 - 40

4x = 140

x = 140 /4

x = 35

Thus, The value of x = 35°

Now,

The first angle = 3x - 12 = 3 * 35 - 12 = 93°

The second angle = 52 + x = 52 + 35 = 87°

As we know that,

Opposite angles of parallelogram are equal .

Therefore,

The angles of parallelogram are 93° , 87° , 93° , 87 ° $.$

Answer 2

Answer:

• All the angles of the parallelogram = 93°,87°,93°,87°

Step-by-step explanation:

Given

• Adjacent angles of A parallelogram are (3x- 12)° and (52+x)°

To Find

• The angles of the Parallelogram

Solution

• We know that sum of adjacent angles of A parallelogram are supplementary.

• So, (3x - 12) + (52 + x) = 180

• Remove brackets

• 3x - 12 + 52 + x = 180

• Add x terms and numerical terms

• 3x + x + -12 + 52 = 180

• 4x + 40 = 180

• Bring 40 to R.H.S

• 4x = 180 - 40

• 4x = 140

• x = $\dfrac{140}{4}$

• x = 35°

So, the angles are

• (3x - 12) = 3 × 35 - 12 = 93°

• 52 + x = 52 + 35 = 87°

So, now Let's find the other two angles of the Parallelogram

• We know that Opposite Angles of a Parallelogram are equal.

• So, the other angles will be 93°,87°

Finally

• All the angles of the parallelogram = 93°,87°,93°,87°

Property's Used

• Adjacent angles of A parallelogram are supplementary

• Adjacent angles of A parallelogram are supplementary Opposite angles of A parallelogram are equal