Question

Adjacent angle of a parallelogram are (3x-150) and (2x+50). Find all the parallelogram

Answer 1

3x-150 + 2x+50 = 180 degree (co interior angles)
5x-100 =180
5x=180+100
5x=280
x=280÷5=56

angles are 18 degree and 150

Answer 2

Given :-

Adjacent angles are 3x+50° and 2x-20°

Need To Find Out :-

The angles of parallelogram.

Solution :-

We know that:-

Adjacent angles of a parallelogram are supplementary i.e their sum is 180°.

$\red{\:{\underline{\boxed{\frak{Sum\: of\: adjacent \: angles_{\:(Parallelogram)} = 180°}}}}}$

$\begin{lgathered}\sf :\implies 3x+50°+2x-20°= 180°\\\end{lgathered}$

$\begin{lgathered}\sf :\implies 3x+2x +50°-20°= 180°\\\end{lgathered}$

$\begin{lgathered}\sf :\implies 5x + 30°=180°\\\end{lgathered}$

$\begin{lgathered}\sf :\implies 5x= 180°-30°\\\end{lgathered}$

$\begin{lgathered}\sf :\implies5x=150°\\\end{lgathered}$

$\begin{lgathered}\sf :\implies x=\dfrac{150°}{5}\\\end{lgathered}$

$\begin{lgathered}\sf :\implies x=\cancel{\dfrac{150°}{5}}\\\end{lgathered}$

$:\implies\red{\boxed{\sf x=30°}}$

As we got the required value of x, let's calculate the angles.

For that, we just have to put the value of x in the given equation of angles.

$\underline{\rm{\sf 1st\:Angle:-}}$

$:\implies \sf 3x+50°$

$:\implies \sf 3(30°)+50°$

$:\implies\sf 90°+50° = \red{140°}$

$\underline{\sf{\sf 2nd \:Angle :- }}$

$:\implies \sf 2x-20°$

$:\implies\sf 2(30°)-20°$

$\begin{lgathered}:\implies 60°-20°=\red{80°}\\\\\end{lgathered}$