8.1 - Intro to Quadrilaterals
Name ________________
1. In quadrilateral ABCD, mA  100 , mB  50 , and mC is 30 more than mD . Find mD
2. The angles of a quadrilateral are x ,  3x  10  , 27 , and  4 x  30  . Find the measure of the largest
angle of the quadrilateral.
3. (a) If two of the angles of a quadrilateral are equal, must the other two angles be equal?
(b) Is it possible for three angles of a quadrilateral to equal each other, but the fourth angle be different?
(c) If all of the angles of a quadrilateral have the same measure, what is this measure?
4. We showed earlier that the interior angles of a convex quadrilateral add to 360 . Show that the interior
angles of a concave quadrilateral sum to 360 as well.
5. The angles of a quadrilateral are in the ratio 14:21:7:3. What is the measure of the smallest exterior
angle?
6. How could you show what the interior angle sum of a convex pentagon? How about a convex hexagon?
7. In quadrilateral ABCD, mA  x , mB  2 x , mC  3x , and mD  4 x . Find the value of x and
state which sides of ABCD must be parallel.
8. The angles of quadrilateral WXYZ are such that mW  mX  mY  mZ . The angles are in an
arithmetic progression, meaning mW  mX  mX  mY  mY  mZ . If mW is four times
the measure of Z , what is m W ?
9. Given: AD = BC, DAB  CBA
D
C
Prove: AC  BD and ADC  BCD
A
B