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WOODWORKING: Oliver Makes Rectangular Blocks like the one shown and then glues them together to make a plaque. Find M1, M2, and M3 so he can cut the pieces of plaque.

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Opposite angles in a rectangle are equal, so angles 1 and 3 are both 67°. Angle 2 is adjacent to the 67° angle and forms a straight line with it, so it measures 180° - 67° = 113°. Therefore, the angle measures are 67°, 113°, and 67°.

Here are the step-by-step instructions with calculations to find the measures of angles 1, 2, and 3 in the woodworking block:

1. Identify the given information:

  • The block is rectangular.
  • One angle is labeled as 67°.

2. Use the properties of rectangles:

  • Opposite angles in a rectangle are congruent.
  • All interior angles in a rectangle add up to 360°.

3. Find m∠1:

  • Angle 1 is opposite to the 67° angle.
  • Therefore, m∠1 = 67° (due to opposite angles being congruent).

4. Find m∠2:

  • Angle 2 is adjacent to the 67° angle and forms a straight line with it.
  • The sum of adjacent angles that form a straight line is 180°.
  • Therefore, m∠2 = 180° - 67° = 113°.

5. Find m∠3:

Angle 3 is also opposite to the 67° angle.

Therefore, m∠3 = 67° (due to opposite angles being congruent).

Summary of the angle measures:

  • m∠1 = 67°
  • m∠2 = 113°
  • m∠3 = 67°

Oliver can now use these angle measures to accurately cut the pieces of the plaque.

The complete question is here:

WOODWORKING: Oliver Makes Rectangular Blocks like the one shown and then glues them-example-1
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