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
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
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°.