Math Problem Statement

Find the values of x, y, and z in the parallelogram with angles 88°, x°, y°, and z°.

Solution

In the given parallelogram, we need to find the values of angles xx, yy, and zz. Here's how we approach this problem:

Key Properties of a Parallelogram:

  1. Opposite angles of a parallelogram are equal.
  2. Adjacent angles in a parallelogram are supplementary (they add up to 180180^\circ).

Solution Steps:

  • The angle labeled 8888^\circ is an adjacent angle to zz^\circ, and since adjacent angles in a parallelogram are supplementary: z=18088=92z = 180^\circ - 88^\circ = 92^\circ

  • Opposite angles are equal in a parallelogram. Therefore: x=z=92x = z = 92^\circ

  • Since yy is opposite to the 8888^\circ angle, we know: y=88y = 88^\circ

Final Values:

  • x=92x = 92^\circ
  • y=88y = 88^\circ
  • z=92z = 92^\circ

Would you like further details on this solution or any related concepts?

Here are some related questions for practice:

  1. What is the sum of all interior angles in any parallelogram?
  2. Can a parallelogram have right angles?
  3. How do you find the area of a parallelogram?
  4. What is the difference between a rhombus and a parallelogram?
  5. How do diagonals behave in a parallelogram?

Tip: Remember, in any parallelogram, opposite angles are always equal, and adjacent angles are supplementary.

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallelogram Properties

Formulas

Adjacent angles in a parallelogram are supplementary (add up to 180°)
Opposite angles in a parallelogram are equal

Theorems

Parallelogram Angle Properties

Suitable Grade Level

Grades 6-8