Question

two adjacent angles of a parallelogram are 3 x minus 4 and 3 X + 16 degree find the value of x and hence find the​

Answer 1

Answer:

Step-by-step explanation:

The value of x is 28° The measure of the angles of the parallelogram are 100°, 80°, 100°, 80°. We know that, sum of the adjacent angles of a parallelogram is 180°.

Answer 2

Question :

Two adjacent angles of a parallelogram are

(3x - 4)° and (3x + 16)°, find the value of x and hence find the two adjacent angles of the Parallelogram.

Given :

• $\bf{\angle_{1}}$ = (3x - 4)°

• $\bf{\angle_{2}}$ = (3x + 16)°

To find :

• The value of x.
• Adjacent of the Parallelogram

Solution :

We know the property of a Parallelogram that the sum of adjacent angles of a Parallelogram is 180°.

$\boxed{\bf{\angle_{1} + \angle_{2} = 180^{\circ}}}$

Now using the above equation and substituting the values in it, we get :

$:\implies \bf{\angle_{1} + \angle_{2} = 180^{\circ}}$

$:\implies \bf{(3x - 4)^{\circ} + (3x + 16)^{\circ} = 180^{\circ}}$

$:\implies \bf{3x - 4^{\circ} + 3x + 16^{\circ} = 180^{\circ}}$

$:\implies \bf{6x + 12^{\circ} = 180^{\circ}}$

$:\implies \bf{6x = - 12^{\circ} + 180^{\circ}}$

$:\implies \bf{6x = 168^{\circ}}$

$:\implies \bf{x = \dfrac{168^{\circ}}{6}}$

$:\implies \bf{x = 28^{\circ}}$

$\boxed{\therefore \bf{6x = 28^{\circ}}}$

Hence, the value of x is 28°.

To find the Adjacent angles of the Parallelogram :

By putting the value of x in the given angles , we can find the required value.

First angle :-

$:\implies \bf{\angle_{1} = (3x - 4)^{\circ}}$

$:\implies \bf{\angle_{1} = (3 \times 28 - 4)^{\circ}}$

$:\implies \bf{\angle_{1} = (84 - 4)^{\circ}}$

$:\implies \bf{\angle_{1} = 80^{\circ}}$

$\boxed{\therefore \bf{\angle_{1} = 80^{\circ}}}$

Hence, the first angle is 80°.

Second angle :-

$:\implies \bf{\angle_{2} = (3x + 16)^{\circ}}$

$:\implies \bf{\angle_{2} = (3 \times 28 + 16)^{\circ}}$

$:\implies \bf{\angle_{2} = (84 + 16)^{\circ}}$

$:\implies \bf{\angle_{2} = 100^{\circ}}$

$\boxed{\therefore \bf{\angle_{2} = 100^{\circ}}}$

Hence, the first angle is 100°.