Question

For 5 points and brainliest to the best correct answer, find the missing measures. Thank you

Answer 1

Answer:

• x = 7
• y = 97°
• z = 19

Step-by-step explanation:

The markings on the figure show this to be a parallelogram. That means opposite sides are congruent. Because the sides are parallel, "alternate interior" angles are also congruent.

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Angle y forms a linear pair with the one marked 83°, so is supplementary to it:

  y = 180°-83° = 97°

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The angle marked y is an exterior angle to the triangle containing the angle marked (7x -5)°. As such, it is equal to the sum of the remote interior angles, the one marked (7x -5)° and the unmarked one that is congruent to (3x +32)°.

  (7x -5) +(3x +32) = 97 . . . . . angle relations in the left-side triangle

  10x +27 = 97 . . . . . . . collect terms

  10x = 70 . . . . . . . . subtract 27

 x = 7 . . . . . . . . divide by 10

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The side marked Z is congruent to the opposite parallel side, so ...

  z = 19

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The missing measures are ...

• x = 7
• y = 97°
• z = 19

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Additional comment

You can also find the value of y by adding up the interior angles of the right-side triangle. The one not shown there is "alternate interior" to the one marked (7x -5)°, hence has the same measure. This gives ...

  (7x -5) +(3x +32) +83 = 180

Subtracting 83° from both sides gives the equation we used above.