The angles are as follows:
- Angle 1 = 50 degrees
- Angle 2 = 50 degrees
- Angle 3 = 130 degrees
- Angle 4 = 130 degrees
To solve this problem, we will use properties of parallelograms and the fact that the sum of the interior angles of any quadrilateral is 360 degrees. Let's go step by step:
Step 1: Identify the Parallelograms
The figure appears to be a quadrilateral with both pairs of opposite sides parallel, which makes it a parallelogram.
Step 2: Name the Parallelogram
Based on the figure, if the angles are right angles, it would be a rectangle. Since one of the angles is given as 50 degrees, it is not a rectangle but a general parallelogram.
Step 3: Find the Measures of the Numbered Angles
- Angle 1: This is given as 50 degrees.
- Angle 2: Since opposite angles in a parallelogram are congruent, angle 2 will also be 50 degrees.
- Angle 3: Adjacent angles in a parallelogram are supplementary (i.e., they add up to 180 degrees), so angle 3 will be 180 - 50 = 130 degrees.
- Angle 4: This is opposite angle 3 and, therefore, is also 130 degrees.
Postulates Used
- The sum of the interior angles of any quadrilateral is 360 degrees.
- Opposite angles in a parallelogram are congruent (equal).
- Adjacent angles in a parallelogram are supplementary.
Calculations
1. Angle 1 = 50 degrees (given).
2. Angle 2 = Angle 1 = 50 degrees (opposite angles are congruent).
3. Angle 3 = 180 degrees - Angle 1 = 180 - 50 = 130 degrees (adjacent angles are supplementary).
4. Angle 4 = Angle 3 = 130 degrees (opposite angles are congruent).
Complete question is here:
For each parallelogram, determine the most precise name AND find the measures of the numbered angles, showing all the work and stating the postulates used.