Introduction to Quadrilaterals

Q.

Angles of a quadrilateral are in the ratio $1:2:3:4$ Find all the angles.

Q. If angles of a quadrilateral are in the ratio of 1:2:3:4, then the largest angle of the quadrilateral is .

1. 150°
2. 108°
3. 144°
4. 72°

Q. Which of the following are convex quadrilaterals?

1. 
2. 
3. 
4. 

Q. What is the sum of all the interior angles of a kite?

1. 540°
2. 360°
3. 90°
4. 180°

Q.

Three angles of a quadrilateral are $75º,90ºand75º$. The fourth angle is

1. $90º$

2. $95º$

3. $105º$

4. $120º$

Q. Question 2 (a)
How many diagonals does each of the following have?
(a) A convex quadrilateral

Q. What are concave quadrilaterals?

1. A quadrilateral with one of its interior angles greater than 180°.
2. A quadrilateral with none of its interior angles greater than 180°.
3. A quadrilateral with one of its interior angles equal to 180°.
4. None of the above

Q.

State and prove the angle sum property of a quadrilateral.

Q. To prove that the sum of angles of hexagon is 720 degree

Q.

If the angles of a quadrilateral are in the ratio 1:2:3:6. Then the largest angle of the quadrilateral is:

1. 144°, 108°, 60°, 48°

2. 144°, 72°, 36°, 108°

3. 30°, 60°, 90°, 120°​

4. 10°, 20°, 30°, 40°

Q. Diagonals of which of the following quadrilaterals does not divide it into two congruent triangles?

1. square
2. rectangle
3. trapezium
4. rhombus

Q. In quadrilateral ABCD, the bisectors of angle A and angle B meet in a point P. If $\angle C={105}^{\circ }$ and $\angle D={55}^{\circ }$, find the measure of angle APB.

1. ${60}^{\circ }$
2. ${70}^{\circ }$
3. ${80}^{\circ }$
4. ${90}^{\circ }$

Q.

Which quadrilaterals have equal diagonals?

Q. The three angles of a quadrilateral are 90°, 60° and 80°. What is the fourth angle?

1. 140°
2. 150°
3. 130°
4. 100°

Q.

If $AB$ and $CD$ are a pair of opposite sides of parallelogram $ABCD$, then

1. $AB=\frac{CD}{2}$
2. $AB=2CD$
3. $AB=CD$
4. $AB=\frac{CD}{3}$

Q.

Question 5
Explain why a rectangle is a convex quadrilateral.

Q.
In the above trapezium ABCD, AB || CD. If $\angle A={50}^{\circ }$ and $\angle B={75}^{\circ }$, then find $\angle C$ and $\angle D.$

1. $\angle C={130}^{\circ },\angle D={105}^{\circ }$
2. $\angle C={90}^{\circ },\angle D={130}^{\circ }$
3. $\angle C={105}^{\circ },\angle D={90}^{\circ }$
4. $\angle C={105}^{\circ },\angle D={130}^{\circ }$

Q. Question 2 (b)
How many diagonals does each of the following have?
(b) A regular hexagon

Q.

The measures of interior angles of a quadrilateral are in the ratio 3:4:5:6. The measure of the largest angle is

1. 120^o

2. 90^o

3. 140^o

4. 130^o

Q. A theatre in a town is built in the form of a kite. It's perimeter is 100 m. If one of the sides measure 20 m. Find the other three sides.

1. $20m,30mand30m$
2. $20m,40mand40m$
3. $20m,20mand30m$
4. $20m,20mand40m$

Q. To form a quadrilateral, out of four points no points are collinear.

1. 1
2. 2
3. 3

Q. Three angles of a quadrilateral are equal. If the fourth angle is twice the value of the equal angles, then find the measure of the fourth angle.

1. ${125}^{\circ }$
2. ${144}^{\circ }$
3. ${154}^{\circ }$
4. ${164}^{\circ }$

Q.

All the angles of a convex quadrilateral are congruent. However, not all its sides are congruent. What type of quadrilateral is it?

1. Parallelogram

2. Trapezium

3. Square

4. Rectangle

Q.

5. Take a point O in the interior of the quadrilateral ABCD. Join O to vertices A, B, C and D. Write the names of the figures in which quadrilateral ABCD will be divided.

Q. Three angles of a quadrilateral are 75°, 90° and 60°, the fourth angle is .

1. 120°
2. 135°
3. 140°
4. 125°

Q.

A convex polygon has at least one diagonal external to it. State true or false.

1. True
2. False

Q. The angles of a quadrilateral are in the ratio $3:5:9:13$. Find the smallest angle.

1. ${24}^{\circ }$
2. ${36}^{\circ }$
3. ${37}^{\circ }$
4. ${45}^{\circ }$

Q. A quadrilateral with only one pair of opposite sides parallel is called a

1. Square
2. Rectangle
3. Parallelogram
4. Trapezium

Q. In a trapezium ABCD, AB || CD. Find $\angle A$ and $\angle B$ if $\angle C={110}^{\circ }$ and $\angle D={125}^{\circ }$.

1. $\angle A={80}^{\circ }$, $\angle B={45}^{\circ }$
2. $\angle A={45}^{\circ }$, $\angle B={80}^{\circ }$
3. $\angle A={70}^{\circ }$, $\angle B={55}^{\circ }$
4. $\angle A={55}^{\circ }$, $\angle B={70}^{\circ }$

Q. In a parallelogram ABCD, $\angle DAB={55}^{\circ }$. Find the angle $\angle CBA$.

1. ${125}^{\circ }$
2. ${135}^{\circ }$
3. ${140}^{\circ }$
4. ${145}^{\circ }$