Question

Parallelogram ABCD is shown below. Ray DE passes through the vertex of ANGLE ADC. What is the measure of ANGLE ADE? (image attached)A. 20 degreesB. 40 degreesC. 50 degreesD. 70 degreesthank you ! :)

Answer 1

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°