Question

question 3
find each angle measure. only enter the numerical value.
(7x + 6)°
(9x − 36)°
m∠aed
m∠deb

Explanation:

Step1: Identify vertical angles

Angles \( \angle AED \) and \( \angle CEB \) are vertical angles? Wait, no, looking at the diagram, \( \angle AED \) and \( \angle CEB \)? Wait, actually, \( \angle AED \) and \( \angle BEC \)? Wait, no, the angles \( (7x + 6)^\circ \) and \( (9x - 36)^\circ \) are vertical angles? Wait, no, actually, \( \angle AED \) and \( \angle BEC \) are vertical? Wait, no, the lines \( AB \) and \( CD \) intersect at \( E \), so \( \angle AED \) and \( \angle BEC \) are vertical? Wait, no, the given angles are \( \angle AED = (7x + 6)^\circ \) and \( \angle CEB = (9x - 36)^\circ \)? Wait, no, the diagram shows \( \angle AED \) as \( (7x + 6)^\circ \) and \( \angle CEB \) as \( (9x - 36)^\circ \)? Wait, no, actually, \( \angle AED \) and \( \angle BEC \) are vertical angles? Wait, no, when two lines intersect, vertical angles are equal. Wait, maybe \( \angle AED \) and \( \angle BEC \) are vertical? Wait, no, the angles \( (7x + 6) \) and \( (9x - 36) \) are vertical angles? Wait, no, maybe \( \angle AED \) and \( \angle BEC \) are vertical, but actually, looking at the diagram, \( \angle AED \) and \( \angle BEC \) are vertical, so they should be equal? Wait, no, maybe \( \angle AED \) and \( \angle CEB \) are vertical? Wait, I think I made a mistake. Wait, the lines \( AB \) and \( CD \) intersect at \( E \), so \( \angle AED \) and \( \angle BEC \) are vertical angles, and \( \angle AEC \) and \( \angle BED \) are vertical angles. Wait, but the given angles are \( \angle AED = (7x + 6)^\circ \) and \( \angle CEB = (9x - 36)^\circ \)? Wait, no, the diagram shows \( \angle AED \) as \( (7x + 6)^\circ \) and \( \angle CEB \) as \( (9x - 36)^\circ \)? Wait, no, maybe \( \angle AED \) and \( \angle BEC \) are vertical, so they are equal. Wait, but maybe \( \angle AED \) and \( \angle BEC \) are vertical, so \( 7x + 6 = 9x - 36 \). Let's solve for \( x \).

Step2: Solve for \( x \)

Set \( 7x + 6 = 9x - 36 \)
Subtract \( 7x \) from both sides: \( 6 = 2x - 36 \)
Add 36 to both sides: \( 42 = 2x \)
Divide by 2: \( x = 21 \)

Step3: Find \( m\angle AED \)

Substitute \( x = 21 \) into \( 7x + 6 \):
\( 7(21) + 6 = 147 + 6 = 153^\circ \)

Step4: Find \( m\angle DEB \)

Since \( \angle AED \) and \( \angle DEB \) are supplementary (they form a linear pair), their sum is \( 180^\circ \).
So \( m\angle DEB = 180 - 153 = 27^\circ \)

Answer:

\( m\angle AED = 153 \)
\( m\angle DEB = 27 \)