Question

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


pls guys hurry up
step by step explanation ​

Answer 1

Answer:

(3x - 4) + (3x + 16) = 180

» 6x + 12 = 180

» 6x = 168

» x = 28

Therefore angles are 80⁰ and 100⁰.

Answer 2

Given : Two adjacent angles of a parallelogram are (3x - 4)° and (3x + 16)°

To Find: Value of x and measure of all angles.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

Let ABCD be the parallelogram in which :

$\: \:$

• ∠A = (3x - 4)°
• ∠C = (3x + 16)°

$\: \: \:$

Here, a parallelogram ABCD is given in which it's two adjacent angles are given. We know that sum of adjacent angles of a parallelogram is 180°.

$\: \: \: \: \:$

$\sf {\underline{★ \:A ccording \: to \: the \: question \: :}}$

$\: \: \:$

$\sf:\implies \: (3x - 4) \degree + (3x + 16) \degree = 180 \degree \\ \\ \\ \sf : \implies \: 3x - 4 + 3x + 16 = 180 \\ \\ \\ \sf:\implies \: 3x + 3x - 4 + 16 = 180 \\ \\ \\ \sf:\implies \: 6x + 12 = 180 \\ \\ \\ \sf:\implies \: 6x = 180 - 12 \\ \\ \\ \sf:\implies \: 6x = 168 \\ \\ \\ \sf:\implies \: x = \cancel\frac{168}{6} \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{x = 28}}} \: \bigstar$

$\: \:$

Put the value of x in the angles.

$\:$

• (3x - 4) = 3(28) - 4 = 80°
• (3x + 16) = 3(28) + 16 = 100°

$\: \:$

So,

$\: \:$

• ∠A = ∠B = 80°
• ∠C = ∠D = 100°

$\: \:$

$\sf\therefore{\underline{Hence, \: all \: angles \: of \: the \: parallelogram \: are \: \bold{100 \degree \: 80 \degree \: \bold{100 \degree}and \: \bold{80 \degree} \: } respectively.}}$