Question

the sum of opposite angles of a parallelogram is 150° find all the angles of the parallelogram

Answer 1

We know that opposite angles of parallelogram are equal.

All the angles of parallelogram add upto 360°


Let the four angles of parallelogram be $\angle{}$A, $\angle{}$B, $\angle{}$C and $\angle{}$D


Let $\angle{}$D be x

So, its opposite is $\angle{}$B

So, $\angle{}$B = x


Let $\angle{}$A be 150°

$\angle{}$C is opposite angle of $\angle{}$A

So, $\angle{}$A = 150°


According to the question,

$\angle{}$A + $\angle{}$B + $\angle{}$C + $\angle{}$D = 360

150° + x + x = 360

2x = 360 - 150

2x = 210

x = $\dfrac{210}{2}$

x = 105



$\therefore{}$ $\angle{}$B => x => 105°

So, $\angle{}$D => x => 105°



$\therefore{}$ m$\angle{}$A = 150°

$\angle{}$C = 150°

$\angle{}$B = 105°

$\angle{}$D = 105°

Answer 2

here is your answer OK ☺☺☺☺☺☺☺

$\huge \red{dear \: friend}$
$\large \pink{we \: know \: that \: paralelogram \: in \: opposite / angle \: are \: equal}$
then some of opposite angles = 150 degree

so we find one angle so divide by 2 = 150/2=75 degree.

$\huge \blue { the \: sum \: of \: the \: angle \: in \: parallelogram \: are \: 360 \: degree}$

so we find other angle so 360 - 150 = 210

it's also opposite to each other so we again divide by 2 = 210/2= 105 degree

then we proof so all angle added...........

one angle + second angle + third angle + fourth angle = 360 degree

75 + 75 + 105 + 105 = 360
360 = 360 degree

OK
$\huge \red {i \: hope \: i \: help \: you}$