The sum of angles in a parallelogram adds up to 360 degrees
The values of x and y are 25 and 15, respectively.
The angles are given as:
[tex]\mathbf{\angle 1 = 4x + 13}[/tex]
[tex]\mathbf{\angle 2 = 4y + 7}[/tex]
[tex]\mathbf{\angle 3 = 3x - 8}[/tex]
[tex]\mathbf{\angle 4= 5x - 12}[/tex]
The opposite angles of a parallelogram are equal.
So, we have:
[tex]\mathbf{4x + 13 = 5x - 12}[/tex]
Collect like terms
[tex]\mathbf{5x - 4x = 13 + 12}[/tex]
[tex]\mathbf{x = 25}[/tex]
Simiarly, we have:
[tex]\mathbf{4y + 7 = 3x -8}[/tex]
Substitute 25 for x
[tex]\mathbf{4y + 7 = 3 \times 25 -8}[/tex]
[tex]\mathbf{4y + 7 = 75 -8}[/tex]
[tex]\mathbf{4y + 7 = 67}[/tex]
Subtract 7 to both sides
[tex]\mathbf{4y = 60}[/tex]
Divide both sides by 4
[tex]\mathbf{y = 15}[/tex]
Hence, the values of x and y are 25 and 15, respectively.
Read more about quadrilaterals at:
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