Angle Sum Property of a Quadrilateral

Q.

Prove that the sum of all the angles of a quadrilateral is ${360}^{\circ }$.

Q.

Three angles of a quadrilateral are ${75}^{\circ },{90}^{\circ }and{75}^{\circ }$. Find the measure of the fourth angle.

Q. The angles of a quadrilateral are x°, (x-10)°, (x+ 30)° and 2x°.Then the value of the greatest angle is degrees.

1. 136
2. 180
3. 68

Q.

In a quadrilateral ABCD, $\angle A+\angle C$is 2 times $\angle B+\angle D$. If $\angle A={140}^{\circ }and\angle D={60}^{\circ },then\angle B=$

1. ${60}^{\circ }$

2. ${80}^{\circ }$

3. ${120}^{\circ }$

4. None of these

Q.

In parallelogram ABCD, if $\angle B-\angle C={40}^{\circ }$, then $\angle A$ is

Q.

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

Q.

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

Q. The four angles of a quadrilateral are in the ratio 2:3:6:7. What is the measures of each angle?

1. 40°, 70°, 120°, 130°
2. 40°, 60°, 120°, 140°
3. 40°, 60°, 110°, 150°
4. 50°, 50°, 120°, 140°

Q.

In a quadrilateral ABCD, CO and DO are the bisector of $\angle Cand\angle D$ respectively.

Prove that $\angle COD=\frac{1}{2}(\angle A+\angle B).$

Q.

If the angles of a quadrilateral are in the ratio 3 :5 : 9 : 13. Then find the measure of the smallest angle.

Q.

The angles of a quadrilateral are in the ratio $2:4:5:7.$ Find the angles.

Q.

ABCD is a parallelogram such that its diagonals are equal.What is the measure of angle ABC?

Q.

Two opposite angles of a parallelogram are $(3x-2)$ and $(63-2x)$.Find all the angles of the parallelogram.

Q.

If an angle of a parallelogram is two thirds of its adjacent angle, the smallest angle of the parallelogram is

(a) ${108}^{\circ }$

(b) ${54}^{\circ }$

(c) ${72}^{\circ }$

(d) ${81}^{\circ }$

Q.

One angle of a parallelogram is 30^o less than twice the smallest angle then the measure of each angle of the parallelogram is

1. 100^o, 80^o, 100^o, 80^o

2. 70^o, 110^o, 70^o, 110^o

3. 120^o, 60^o, 120^o, 60^o

4. 40^o, 140^o, 40^o, 140^o

Q.

Prove that if the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.

Q. Question 12
Can all the angles of a quadrilateral be right angles ? Give reason for you answer.

Q.

In the given figure, O is the centre of a circle. If $\angle AOB={100}^{\circ }and\angle AOC={90}^{\circ }then\angle BAC=?$

(a) ${85}^{\circ }$

(b) ${80}^{\circ }$

(c) ${95}^{\circ }$

(d) ${75}^{\circ }$

Q. Question 169
In the figure, find the value of x.

Q.

If the degree measures of the angles of quadrilateral are 4x, 7x, 9x and 10x, what is the sum of the measures of the smallest angle and largest angle ?

1. ${140}^{\circ }$

2. ${150}^{\circ }$

3. ${168}^{\circ }$

4. ${180}^{\circ }$

Q.

If the bisectors of two adjacent angles A and B of a quadrilateral ABCD intersect at a point O such that $\angle C+\angle D=k\left(\angle AOB\right)$, then find the value of k.

Q.

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1:2:4:5. Find the measure of each angle of the quadrilateral.

Q.

In a parallelogram ABCD, if ∠A = 115^o, then ∠B, ∠C and ∠D are

1. ∠B = 55^o, ∠C = 105^o, ∠D = 65^o

2. ∠B = 60^o, ∠C = 135^o, ∠D = 75^o

3. ∠B = 45^o, ∠C = 120^o, ∠D = 65^o

4. ∠B = 65^o, ∠C = 115 ^o, ∠D = 65^o

Q.

One angle of a hexagon is 120^o. The other five angles are equal to each other. The measure of each equal angle is

1. 135^o

2. 100^o

3. 125^o

4. 120^o

Q.

Three angles of a quadrilateral are respectively equal to ${110}^{\circ },{50}^{\circ }$ and ${40}^{\circ }$. Find its fourth angle.

Q.

In a quadrilateral ABCD, bisectors of A and B intersect at O such that $\angle AOB={75}^{\circ }$, then write the value $\angle C+\angle D$.

Q. The opposite angles of a parallelogram are $(3x-2{)}^{\circ }$ and $(x+48{)}^{\circ }$. What is the value of $x$?

1. 25

Q. The sum of angles of a kite is:

1. ${180}^{\circ }$​
2. ${360}^{\circ }$​
3. ${480}^{\circ }$​
4. ${90}^{\circ }$​

Q.

Maximum exterior angle possible for a regular polygon is

1. 60^o

2. 120^o

3. 180^o

4. 100^o

Q.

Two adjacent angles of a parallelogram are in the ratio 2: 3, the measure of angles will be

1. 90^o, 90^o, 90^o, 90^o

2. 72^o, 108^o, 72^o, 108^o

3. 70^o, 110^o, 70^o, 110^o

4. 80^o, 100^o, 80^o, 100^o