quadrilateral + degrees

tonebeeze wrote:I know this problem is not that difficult, however I am having trouble charting/visualizing this problem.

In quadrilateral ABCD , AB = CD and BC = AD . If angle CBD = 30 degrees and angle BAD = 80 degrees, what is the value of angle ADC?


a. 30 degrees
b. 50 degrees
c. 70 degrees
d. 100 degrees
e. 120 degrees

OAis B

I am getting D

In the figure below, ABCD is a quadrilateral.

Triangle ABD and triangle BCD are congruent.
Thus, Angle A = Angle C = 80
Angle CBD = Angle ADB = 30
Angle ABD = Angle CDB = 70

Thus, angle ADC = Angle ADB + Angle BDC = 30 + 70 = 100

tonebeeze wrote:I know this problem is not that difficult, however I am having trouble charting/visualizing this problem.

In quadrilateral ABCD , AB = CD and BC = AD . If angle CBD = 30 degrees and angle BAD = 80 degrees, what is the value of angle ADC?


a. 30 degrees
b. 50 degrees
c. 70 degrees
d. 100 degrees
e. 120 degrees

OAis B

This is based on congruent triangles. the diagonal BD divides the quadrilateral into two triangles namely ABD and BDC. diagonal BD is a common side to both triangles, while the other two sides are equal ,i.e. AD=BC and AB=CD. Thus, the two triangles are congruent, because they have 3 sides that are equal.

angle BAC = angle BCD = 80

angle BDC = 180-30-80=70

angle ADB =Angle CBD = 30 (angle opposite to equal sides between congruent triangles)

angle ADC = angle ADB + angle BDC = 30 + 70 = 100 degrees.

The correct answer should be D