Given:
• m∠B = 70 degrees
,
• m∠AOE = 130 degrees
Let's find the measure of angle ADE, m∠ADE.
Apply the angle properties of a parallelogram.
Adjacent angles of a parallelogram are supplementary and supplementary angles sum up 180 degrees.
• Thus, we have:
m∠A + m∠B = 180
m∠A = 180 - m∠B
m∠A = 180 - 70
m∠A = 110 degrees
Let O be the point of intersection of the ray DE and the parallelogram.
ADO forms a triangle.
• 130 degrees form a linear pair with angle DOA.
Linear pair of angles are supplementary.
Thus, we have:
m∠ DOA. = 180 - 130 = 50 degrees.
Now, apply the Triangle Angle Sum theorem to find m∠ADE.
m∠ADE + m∠DOA + m∠A = 180
m∠ADE + 50 + 110 = 180
m∠ADE + 160 = 180
Subtract 160 from both sides:
m∠ADE + 160 - 160 = 180 - 160
m∠ADE = 20 degrees
Therefore, the measure of angle ADE is 20 degrees.
ANSWER:
A. 20°
