Question

lesson 19 practice problems

1. what is the measure of angle abe?
2. select all true statements about the figure.

a. c + b = d + c
b. d + b = 180
c. rotate clockwise by angle abc using center b. then angle cbd is the image of angle abe.
d. rotate 180 degrees using center b. then angle cbd is the image of angle eba.
e. reflect across the angle bisector of angle abc. then angle cbd is the image of angle abe.
f. reflect across line ce. then angle cbd is the image of angle eba

Explanation:

Step1: Find angle ABE in first - part

Vertical angles are equal. Angle ABE and the 40 - degree angle are vertical angles. So, $\angle ABE = 40^{\circ}$.

Step2: Analyze statements in second - part

• Statement A:
• Given $c + b=d + c$. Subtract $c$ from both sides, we get $b = d$. Since $b$ and $d$ are vertical angles, they are equal. So, $c + b=d + c$ is True.
• Statement B:
• $d$ and $b$ are vertical angles, not supplementary. So, $d + b = 180$ is False.
• Statement C:
• Rotating clock - wise by angle $ABC$ using center $B$ will not map angle $ABE$ to angle $CBD$. So, this statement is False.
• Statement D:
• Rotating 180 degrees using center $B$ maps angle $EBA$ to angle $CBD$. This is True because a 180 - degree rotation about a point maps an angle to its vertical angle.
• Statement E:
• Reflecting across the angle bisector of angle $ABC$ will not map angle $ABE$ to angle $CBD$. So, this statement is False.
• Statement F:
• Reflecting across line $CE$ will not map angle $EBA$ to angle $CBD$. So, this statement is False.

Answer:

1. $40^{\circ}$
2. A. $c + b=d + c$, D. Rotate 180 degrees using center $B$. Then angle $CBD$ is the image of angle $EBA$.