Question

use the parallelogram abcd to solve problems 1 through 7. you can double-click on the figure to mark it. each question is worth 2 points.
help video for questions 1 through 7.
need help identifying the angles? watch this help video

1. what do we know about alternate interior angles of parallel lines?

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1. what do we know about the measure of the alternate interior angles eab and aed?

choose an answers $m\angle eab = 25^\circ$, what is the measure of $m\angle aed$?

1. angle bea and angle ead are also alternate interior angles. $m\angle bea = 30^\circ$, what is the measure of angle ead?
2. what is the measure of angle dab? justify your answer.
3. what do we know about the measure of the opposite angles dab and deb?

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1. what do we know about the measure of the adjacent angles $\angle dab$ and $\angle ade$?

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1. what is the measure of angle ade?

Explanation:

Step1: Recall alternate interior angles rule

Alternate interior angles formed by a transversal cutting parallel lines are congruent.

Step2: Recall consecutive angles rule

Consecutive angles in a parallelogram are supplementary (sum to $180^\circ$).

Step3: Solve Q1: Alternate interior angles property

Alternate interior angles (formed by a transversal across parallel lines) are equal in measure.

Step4: Solve Q2: Apply congruent alternate angles

Since $\angle EAB$ and $\angle AED$ are alternate interior angles, $m\angle AED = m\angle EAB = 25^\circ$

Step5: Solve Q3: Apply congruent alternate angles

Since $\angle BEA$ and $\angle EAD$ are alternate interior angles, $m\angle EAD = m\angle BEA = 30^\circ$

Step6: Solve Q4: Calculate $\angle DAB$

$m\angle DAB = m\angle EAB + m\angle EAD = 25^\circ + 30^\circ = 55^\circ$

Step7: Solve Q5: Opposite angles property

In a parallelogram, opposite angles are congruent, so $m\angle DAB = m\angle BCD$.

Step8: Solve Q6: Adjacent angles property

In a parallelogram, adjacent angles are supplementary, so $m\angle DAB + m\angle ADE = 180^\circ$.

Step9: Solve Q7: Calculate $\angle ADE$

$m\angle ADE = 180^\circ - m\angle DAB = 180^\circ - 55^\circ = 125^\circ$

Answer:

1. Alternate interior angles are congruent (equal in measure).
2. $m\angle AED = 25^\circ$
3. $m\angle EAD = 30^\circ$
4. $m\angle DAB = 55^\circ$; Justification: It is the sum of $\angle EAB$ and $\angle EAD$, which are alternate interior angles with $\angle AED$ and $\angle BEA$ respectively.
5. In parallelogram $ABCD$, opposite angles $\angle DAB$ and $\angle BCD$ are congruent (equal in measure).
6. In parallelogram $ABCD$, adjacent angles $\angle DAB$ and $\angle ADE$ are supplementary (their measures sum to $180^\circ$).
7. $m\angle ADE = 125^\circ$