In the given parallelogram ABCD
what is the value of 2x + y
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In the given parallelogram ABCD
what is the value of 2x + y
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[tex]\textbf{To find:}[/tex]
[tex]\textsf{The value of 2x+y from the figure}[/tex]
[tex]\textbf{Solution:}[/tex]
[tex]\underline{\textsf{Concept used:}}[/tex]
[tex]\textsf{1.Opposite angles of parallelogram are equal}[/tex]
[tex]\textsf{2.Sum of adjacent angles of parallelogram are supplementary}[/tex]
[tex]\textsf{By using property (1)}[/tex]
[tex]\mathsf{3x+15=2x+35}[/tex]
[tex]\mathsf{3x-2x=35-15}[/tex]
[tex]\implies\boxed{\mathsf{x=20^\circ}}[/tex]
[tex]\textsf{By using property (2)}[/tex]
[tex]\mathsf{2x+35+2y+15=180^\circ}[/tex]
[tex]\mathsf{2x+2y+50^\circ=180^\circ}[/tex]
[tex]\mathsf{2x+2y=180^\circ-50^\circ}[/tex]
[tex]\mathsf{2x+2y=130^\circ}[/tex]
[tex]\mathsf{x+y=65^\circ}[/tex]
[tex]\mathsf{20^\circ+y=65^\circ}[/tex]
[tex]\mathsf{y=65^\circ-20^\circ}[/tex]
[tex]\implies\boxed{\mathsf{y=45^\circ}}[/tex]
[tex]\mathsf{Now,}[/tex]
[tex]\mathsf{2x+y=2(20^\circ)+45^\circ=85^\circ}[/tex]
[tex]\textbf{Answer:}[/tex]
[tex]\mathsf{The\;value\;of\;2x+y\;is\;85^\circ}[/tex]