Question

Two adjacent angle of a parallelogram are (2x+25) and (3x-5). The value of x is

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

$\textbf{\underline{Two\;adjacent\;angle\;of\; parallelogram}}$

= (2x + 25) and (3x - 5)

So,

${\boxed{\sf\:{Sum\;of\;adjacent\;angle\;of\; parallelogram =180}}}$

2x + 25 + 3x - 5 = 180°

5x + 20 = 180

5x = 180 - 20

5x = 160

$\rm \: \: \: \: \: \: \: \: \:x=\dfrac{\cancel{160}}{\cancel{5}}$

x = 32°

So,

$\Large{\boxed{\bigstar{{Adjacent\;angles:-}}}}$

= (2x + 25)

= 2 × 32 + 25

= 64 + 25

= 89°

Also,

= (2x + 25)

= 2 × 32 + 25

= 64 + 25

= 89°

Also,

= (3x - 5)

= 3 × 32 - 5

= 96 - 5

= 91°

Answer 2

Answer

Given,

• Adjacent angles of a parallelogram are (2x + 25) & (3x - 5)

To find,

• The value of 'x'

Solution ,

Firstly I will give some properties of a parallelogram so that you may become familiar to it.

⚝ Parallelogram

࿇ Opposite sides are congruent (equal)

࿇ Opposite angels are congruent (equal)

࿇ Adjacent angles are supplementary.(sum of angle is 180°)

࿇ The diagonals of a parallelogram bisect each other.

࿇ Each diagonal of a parallelogram divides it into two congruent triangles.

Now we got that adjacent angle of a parallelogram is supplementary.

Hence,

⇛ (2x + 25) + (3x - 5) = 180°

⇛ 5x + 20 = 180

⇛ 5x = 160

⇛x = $\sf \frac { 160 } { 5 }$

⇛ x = 32°

So let us place the value of x in both the angles to get their measurements.

⇰ 1st angle

⇛ (2x + 25)

⇛ 2(32) + 25

⇛ 64 + 25

⇛ 89°

⇰ 2nd angle

⇛ (3x - 5)

⇛ 3(32) - 5

⇛96 - 5

⇛91°