Question

The adjacent angles of a parallelogram are (5x-11) degrees and (3x-9) degrees . Find all the angles of the parallelogram . Answer the question with full working . If you answer this question I will mark you as brain list

Answer 1

Answer:

• the angles in the parallelogram are 114°, 66°,114°,66°

Step-by-step explanation :

Given:

• The adjacent angles of a parallelogram are (5x-11) degrees and (3x-9) degrees

To Find:

• the measures of all the angles in the parallelogram

Solution:

We know that the sum of any two adjacent angles in a parallelogram equals 180°

Here,

The angles 5x - 11 and 3x - 9 are adjacent angles in the parallelogram

Now,

Let's frame an equation adding up the angles and balance the R.H.S with 180°

Framing an equation,

$\longrightarrow \sf (5x - 11 )\degree + (3x - 9)\degree = 180\degree$

$\longrightarrow \sf 5x + 3x - 11 - 9 \degree = 180\degree$

$\longrightarrow \sf 8x - 20 \degree = 180\degree$

$\longrightarrow \sf 8x = 180\degree-20\degree$

$\longrightarrow \sf 8x = 200\degree$

$\longrightarrow \sf x = \cancel\dfrac{200}{8}$

$\longrightarrow \sf {\purple{\underline{\boxed{\frak{x = 25 \degree}}}\star}}$

Let's find the measure of the angles,

$\longrightarrow \sf 5x - 11 = 5(25) -11 = 144\degree$

$\longrightarrow \sf 3x - 9 = 3(25) -9 = 66\degree$

∴ The measures of the angles are 114, 66 ,114 ,66°