Left Panel Interactive

Statements

Reasons

1. Draw segment AD

1. unique line postulate

2. ∠1 is an exterior ∠ of △ADE

2. def. of exterior angle

3. m∠1 = m∠D + m∠A

3. exterior angles theorem

4. #&m\angle{\sf D} = \frac{\sf 1}{\sf 2}x#&

4.inscribed angle theorem

5. #&m\angle{\sf A} = \frac{\sf 1}{\sf 2}y#&

5.inscribed angle theorem

6. #&m\angle{\sf 1} = \frac{\sf 1}{\sf 2}x + \frac{\sf 1}{\sf 2}y#&

6. substitution property

7. #&m\angle{\sf 1} = \frac{\sf 1}{\sf 2}(x + y)#&

7. distributive property