Question

1. what is the length of (overline{ae}) when (e) is the midpoint of (overline{ag})?

options: 7, 24, 35, 48

1. in the figure, (overrightarrow{ed}) and (overrightarrow{ea}) are opposite rays, and (overrightarrow{eb}) bisects (angle aec).

if (mangle aec = 108^circ) and (mangle aeb=(6x)^circ), then what is the value of (x)?
(x=)

1. (mangle aeb = 37^circ), what is (mangle ced)?

(mangle ced=) (circ)

1. identify the alternate interior, consecutive interior, and corresponding angles for (angle 1) by dragging the label to the correct location in the diagram.

• alternate interior angle
• consecutive interior angles
• corresponding angle

Explanation:

Question 9

Step1: Since E is the midpoint of \( \overline{AG} \), \( AE = EG \).

So, \( 3x + 3 = 5x - 11 \)

Step2: Solve for x.

Subtract \( 3x \) from both sides: \( 3 = 2x - 11 \)
Add 11 to both sides: \( 14 = 2x \)
Divide by 2: \( x = 7 \)

Step3: Find the length of \( \overline{AE} \).

Substitute \( x = 7 \) into \( 3x + 3 \): \( 3(7) + 3 = 21 + 3 = 24 \)

Step1: Since \( \overrightarrow{EB} \) bisects \( \angle AEC \), \( \angle AEB = \angle BEC \).

And \( \angle AEC = 108^\circ \), so \( \angle AEB = \frac{108^\circ}{2} = 54^\circ \)

Step2: Given \( m\angle AEB = (6x)^\circ \), set \( 6x = 54 \)

Step3: Solve for x.

Divide both sides by 6: \( x = \frac{54}{6} = 9 \)

Step1: From the diagram, \( \angle AEB + \angle BEC + \angle CED = 180^\circ \) and \( \angle BEC = 90^\circ \) (right angle).

Step2: Substitute \( m\angle AEB = 37^\circ \) and \( \angle BEC = 90^\circ \) into the equation.

\( 37^\circ + 90^\circ + m\angle CED = 180^\circ \)

Step3: Solve for \( m\angle CED \).

\( 127^\circ + m\angle CED = 180^\circ \)
Subtract \( 127^\circ \) from both sides: \( m\angle CED = 180^\circ - 127^\circ = 53^\circ \)

Answer:

24

Question 10