Parallelogram JKLM has angle measures J(2 x +9) and M(6 x -1) determine the measure of angle k

The sum of opposite angle and sides of a parallelogram is 180 . If a parallelogram JKLM has angle measures J(2 x +9) and M(6 x -1), then <J + < M = 180

Substitute:

2 x +9+6x-1 = 180

collect like terms;

2x+6x+9-1 = 180

8x+8 = 180

8x = 180-8

8x = 172

x = 172/8

x = 21.8°

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MrRoyal MrRoyal · Answer 2 · 2021-12-16T12:47:09+01:00

For the shape to be a quadrilateral, then the measure of angle k must 128 degrees

For quadrilateral PQRS to be an actual quadrilateral, then:

[tex]K = M[/tex] --- opposite angles of quadrilateral

[tex]J + M= 180[/tex] --- adjacent angles of quadrilateral

[tex]J + M = 180[/tex] implies that:

[tex]2x + 9 + 6x -1 = 180[/tex]

Collect like terms

[tex]2x + 6x = 180 -9 +1[/tex]

[tex]8x = 172[/tex]

Divide both sides by 8

[tex]x = 21.5[/tex]

We have:

[tex]K = M[/tex]

This becomes

[tex]K = 6x -1[/tex]

Substitute 21.5 for x

[tex]K = 6\times 21.5 -1[/tex]

[tex]K = 129 -1[/tex]

Subtract 1 from 129

[tex]K = 128[/tex]

Hence, the measure of angle K must be 128 degrees