Understanding Quadrilaterals
Exercise 3
1. Given a parallelogram ABCD. Complete each statement along with the definition or property used.
2. Consider the following parallelograms. Find the values of the unknowns x, y, z.
(i)
(ii)
Answer: x, y and z will be complementary to 50°.
So, Required angle = 180°  50° = 130°
(iii)
Answer: z being opposite angle= 80°
x and y are complementary, x and y
= 180°  80° = 100°
(iv)
Answer: As angles on one side of a line are always complementary
So, x = 90°
So, y = 180°  (90° + 30°) = 60°
The top vertex angle of the above figure = 60° x 2=120°
Hence, bottom vertex Angle = 120° and
z = 60°
(v)
Answer: y= 112°, as opposite angles are equal in a parallelogram
x= 180°(112°40°)=28°
As adjacent angles are complementary so angle of the bottom left vertex
=180°112°=68°
So, z=68°40°=28°
Another way of solving this is as follows:
As angles x and z are alternate angles of a transversal so they are equal in measurement.
3. Can a quadrilateral ABCD be a parallelogram if
Answer: (i)It can be , but not always as you need to look for other criteria as well.
(ii) In a parallelogram opposite sides are always equal, here AD BC, so its not a parallelogram.
(iii) Here opposite angles are not equal, so it is not a parallelogram.
5. The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.
Answer: Opposite angles of a parallelogram are always add upto 180°.
6. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
Answer: 90°, as they add up to 180°
7. The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
Answer: Angle opposite to y = 180°  70°=110°
Hence, y = 110°
x = 180°  (110° + 40°) = 30°, (triangle’s angle sum)
z = 30° (Alternate angle of a transversal)
8. The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)
Answer: As opposite sides are equal in a parallelogram
Answer: As you know diagonals bisect each other in a parallelogram.
9. In the given figure both RISK and CLUE are parallelograms. Find the value of x.
Answer: In parallelogram RISK
