Question

Find the value of x, y, and z in the parallelogram below.

Answer 1

• x = 67
• y = 121
• z = 65

Explanation:

You want to know the values of x, y, and z in the parallelogram with angle (y -9)° opposite the one marked 112°, and angles (x +1)° and (z +3)° adjacent to the one marked 112°.

Parallelogram

In a parallelogram, opposite angles are congruent, and adjacent angles are supplementary. This means ...

112° = (y -9)°

121 = y . . . . . . . divide by °, add 9

and

180° -112° = (x +1)°

68 = x +1 . . . . . . . . divide by °

67 = x . . . . . . . . . subtract 1

and

180° -112° = (z +3)°

68 = z +3 . . . . . . . . divide by °

65 = z . . . . . . . . . subtract 3

The values of x, y, and z are 67, 121, and 65, respectively.

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