Quadrilaterals

Q. Find the measure of each exterior angle of a 9-sided regular polygon.

1. 30°
2. 40°
3. 50°
4. 45°

Q. The angles of a quadrilateral are in the ratio of 2 : 3 : 5 : 8. Find the measure of each angle.

Q.

Is it possible to have a regular polygon if its interior angle measures ${170}^{\circ }$?

1. AD and DC

2. BD only

Q. The angles of a quadrilateral are in ratio 1 : 3 : 7 :9 find the measure of each angle.

Q. The angle sum of a convex polygon with n number of sides is given by:

1. (n + 2) $\times$ 180°
2. (n - 2) $\times$ 180°
3. (2n + 2) $\times$ 180°
4. (2n + 4) $\times$ 180°

Q.

Assertion: If the angles of a quadrilateral are in the ratio $2:3:7:6,$ then the measure of angles are $40º60º,140º,120º$respectively.

Reason: The sum of the angles of a quadrilateral is $360º.$

1. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

2. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

3. If Assertion is correct but Reason is incorrect.

4. If Assertion is incorrect but Reason is correct.

Q.

Name the point where two sides of a triangle meet.

Q. If out of four points no three are collinear, then we get a .

1. line
2. triangle
3. quadrilateral

Q.

The angles of a quadrilateral are $x^{\circ },(x-10{)}^{\circ },(x+30{)}^{\circ }$ and $(2x{)}^{\circ }$. Find the value of the greatest angle.

1. ${136}^{\circ }$

2. None of these

3. ${180}^{\circ }$

4. ${68}^{\circ }$

Q.

Rohan marked 7 points on a plane paper. Which of the following combinations result in a quadrilateral (all points need to be joined)?

1. 2 only

2. 2, 4 only

3. 2, 3, 4 only

4. All of them

Q. Question 183
Find the maximum number of acute angles which a convex quadrilateral, a pentagon and a hexagon can have. Observe the pattern and generalise the result for any polygon.

Q. How many maximum reflex interior angles can a quadrilateral have?

1. $2$
2. $1$
3. $3$
4. There cannot be any reflex interior angle in quadrilateral

Q. If |z|+2=I(z), then z= (x, y) lies on-

Q.

How many vertices are included in any side of a triangle?

1. 0

2. 2

3. 3
4. 1

Q.

Draw rough diagrams of two angles such that they have

(a) One point in common.

(b) Two points in common.

(c) Three points in common.

(d) Four points in common.

(e) One ray in common.

Q. Find the measure of each exterior angle of a 9-sided regular polygon.

1. 30°
2. 40°
3. 50°
4. 45°

Q.

A parallelogram $PQRS$ is constructed with sides $QR=6cm$, $PQ=4cm$ and $\angle PQR=90°$. Then $PQRS$ is a

1. Square

2. Rectangle

3. Rhombus

4. Trapezium

Q.

If a quadrilateral is cyclic, how many vertices of it should lie on the circle?

1. 1

2. 3
3. 2
4. 4

Q. Question 2
Is it possible to have a polyhedron with any given number of faces?

Q. Question 5 (b)
(b) Can it be an interior angle of a regular polygon? Why?

Q. Fill in the blanks:
(i) A quadrilateral has ......... sides.
(ii) A quadrilateral has ......... angles.
(iii) A quadrilateral has ......... vertices, no three of which are .........
(iv) A quadrilateral has ......... diagonals.
(v) A diagonal of a quadrilateral is a line segment that joins two ......... vertices of the quadrilateral.
(vi) The sum of the angles of a quadrilateral is.........

Q.

Which of the following does not have a diagonal?

1. Triangle

2. Quadrilateral

3. Pentagon

4. None of these

Q.

Tell whether the blue figure is a translation of the red figure.

Q. The ratio between exterior angle and interior angle of a regular polygon is 1 : 5. Find the number of sides of the polygon.

Q. (i) Is it possible to have a regular polygon with a measure of each exterior angle ‘a’ as 22°?
(ii) Can it be an interior angle of a regular polygon? Why?

Q. The quadrilateral whose diagonals are equal and bisect each other at right angle?

Q. If three angles a quadrilateral are ${100}^{\circ }$, ${90}^{\circ }$ and ${60}^{\circ }$, then the fourth angle will be ________.

1. ${100}^{\circ }$
2. ${120}^{\circ }$
3. ${150}^{\circ }$
4. ${110}^{\circ }$

Q.

Find the area of quadrilateral ABCD in sq.units. Given AE = 5 units, BD =8 units and CF = 4 units

1. 144 sq. units

2. 36 sq. units

3. 20 sq. units

4. Data insuficient

Q. Question 1 (i)
Can a polyhedron have three triangles on its faces?

Q. $\text{ABCD}$ is a rhombus. If $\angle \text{DAC}={25}^{\circ }$, then the measure of $\angle \text{ABC}$ is.

1. ${155}^{\circ }$
2. ${130}^{\circ }$
3. ${65}^{\circ }$