Each trapezoid is isosceles. Find the measure of each angle. 1. 2. 3. 3 2 111° 77° R 4. Y 105° X Z W 5. T3 65° S 6. 1 A B 60° 2 49⁰ C D

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### Isosceles Trapezoids: Finding Angle Measures

**Problem Statement:**

Each trapezoid is isosceles. Find the measure of each angle.

**Trapezoid 1:**
```
Top Side (not labeled with angle measures or lengths)

   3              2

77°              1
 _____________
  Bottom Side (base)
```
**Explanation:**
- The top and bottom angles are opposite each other.
- The measures of the top and bottom angles must add up to 180° because of the linear pair relationship.

Using the property of isosceles trapezoids:
- Base angles are equal, thus if one base angle is 77°, then the other base angle is 77°.
- The upper angles are congruent too: 180° - 77° = 103° each.

**Trapezoid 2:**
```
Top

   1

111°          1
 -  POS - 
   3           2
```
**Explanation:**
- Similar deduction as Trapezoid 1.
- If the lower angle is 111°, then the other lower angle is 111°.
- The top angles are both equal to: 180° - 111° = 69° each.

**Trapezoid 3:**
```
Top

   2          3

                  49° 
 1
```
**Explanation:**
- Given the properties of isosceles trapezoids, you can find the top angles as follows:
- 49° on the bottom left then,
- The others are: 180° - 49° = 131° each for the top angles.
- Since it is isosceles, angles on the top are equal.

**Trapezoid 4:**
```
 Z
   1             1

  105°           X
   W            
Y  
```
**Explanation:**
- If one base angle is 105°, then the other base angle shall be 105°.
- The top angles of isosceles trapezoids measure: 180° - 105° = 75° each.

**Trapezoid 5:**
```
Q                 R

 1             1     
65°    
P                S
```
- If one angle at the base is
Transcribed Image Text:### Isosceles Trapezoids: Finding Angle Measures **Problem Statement:** Each trapezoid is isosceles. Find the measure of each angle. **Trapezoid 1:** ``` Top Side (not labeled with angle measures or lengths) 3 2 77° 1 _____________ Bottom Side (base) ``` **Explanation:** - The top and bottom angles are opposite each other. - The measures of the top and bottom angles must add up to 180° because of the linear pair relationship. Using the property of isosceles trapezoids: - Base angles are equal, thus if one base angle is 77°, then the other base angle is 77°. - The upper angles are congruent too: 180° - 77° = 103° each. **Trapezoid 2:** ``` Top 1 111° 1 - POS - 3 2 ``` **Explanation:** - Similar deduction as Trapezoid 1. - If the lower angle is 111°, then the other lower angle is 111°. - The top angles are both equal to: 180° - 111° = 69° each. **Trapezoid 3:** ``` Top 2 3 49° 1 ``` **Explanation:** - Given the properties of isosceles trapezoids, you can find the top angles as follows: - 49° on the bottom left then, - The others are: 180° - 49° = 131° each for the top angles. - Since it is isosceles, angles on the top are equal. **Trapezoid 4:** ``` Z 1 1 105° X W Y ``` **Explanation:** - If one base angle is 105°, then the other base angle shall be 105°. - The top angles of isosceles trapezoids measure: 180° - 105° = 75° each. **Trapezoid 5:** ``` Q R 1 1 65° P S ``` - If one angle at the base is
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