Math, asked by aradhyaraj345, 11 months ago

Two adjacent angles of a parallelogram are (3x–4)° and (3x+16)°. Find the value of x and hence find the measure of each of its angles.

please solve it to easily way​

Answers

Answered by ShobhitD
12

Answer:

3x-4 = 80° , 3x+16 = 100°

Step-by-step explanation:

since adjacent angles of parallelogram are supplementary

(3x-4)°+(3x+16)° = 180°

6x + 12= 180

6x = 168

x = 168/6

x = 28

Answered by Anonymous
16

The value of x is 28°.

The measure of the angles of the parallelogram are_  100°, 80°, 100°, 80°.

Step-by-step explanation:

It is given that,

The measurement of the adjacent angles of a parallelogram are_

(3x-4)° and

(3x+16)°

We know that, sum of the adjacent angles of a parallelogram is 180°.

∴ (3x-4)° + (3x+16)° = 180°

⇒ 3x° - 4° + 3x° + 16° = 180°

⇒ 3x° +3x° +16° - 4° = 180°

⇒ 6x° + 12° = 180°

⇒ 6x° = 180° - 12°

⇒ 6x° = 168°

⇒ x° = 168°/6

⇒ x° = 28°

∴ x = 28°

∴ The measure of one of the adjacent angle = (3x-4)°

                                                                         = (3*28 - 4)°

                                                                        = (84- 4)°

                                                                        = 80°

∴ The measure of the co-interior angle of this adjacent angle_

(180 - 80)° [∵ sum of the co-interior angle is 180°]

= 100°

The measure of the other adjacent angle = (3x+16)°

                                                                     =(3*28 +16)°

                                                                     = (84+16)°

                                                                    = 100°

∴ The measure of the co-interior angle of this angle-

(180-100)° [∵Sum of the co-interior angle is 180°]

= 80°

∴ The value of x is 28° and the measure of the angles of the parallelogram are 100°, 80°, 100°, 80°.

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