If two adjacent angles of a parallelogram ABCD are in the ratio 5:4 find all the angles of the parallelogram
Answers
Step-by-step explanation:
sum of angles of a quadrilateral is equals to 360 degree .
hence the angles of the given quadrilateral must sum up to give 360 .
Hence, adding all the angles with variable X we can obtain as follows :-
\begin{gathered}x + 20 + x - 20 + 2x + 5 + 2x - 5 = 360 \\ \\ \\ \\ x + x + 2x + 2x = 360 \\ \\ \\ \\ 6x = 360 \\ \\ \\ x = \frac{360}{6} \\ \\ \\x = 60\end{gathered}
x+20+x−20+2x+5+2x−5=360
x+x+2x+2x=360
6x=360
x=
6
360
x=60
hence, we got x is equals to 60 degrees and putting the value of x in the variable equations given for each angle we can obtain as follows :-
\begin{gathered}x + 20 = 60 + 20 = 80 \\ \\ x - 20 = 60 - 20 = 40 \\ \\ \\ 2x - 5 = 120 - 5 = 115 \\ \\ \\ 2x + 5 = 120 + 5 = 125\end{gathered}
x+20=60+20=80
x−20=60−20=40
2x−5=120−5=115
2x+5=120+5=125
these are the four angles of the quadrilateral given