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: