Angle Sum Property of Quadrilateral

Q.

The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.

1. ${35}^{\circ }$, ${65}^{\circ }$, ${95}^{\circ }$, ${125}^{\circ }$​

2. ${15}^{\circ }$, ${105}^{\circ }$, ${130}^{\circ }$, ${40}^{\circ }$​

3. ${145}^{\circ }$, ${105}^{\circ }$, ${65}^{\circ }$, ${45}^{\circ }$

4. ${135}^{\circ }$, ${105}^{\circ }$, ${75}^{\circ }$, ${45}^{\circ }$​

Q.

Three angles of a quadrilateral are equal and the measure of the fourth angle is ${120}^{\circ }$. Find the measure of each of the equal angles.

1. ${240}^{\circ }$

2. ${100}^{\circ }$

3. ${135}^{\circ }$

4. ${80}^{\circ }$

Q.

If an angle of a parallelogram is two-third of its adjacent angle, then the smallest angle of the parallelogram is

1. ${55}^{\circ }$

2. ${65}^{\circ }$

3. ${72}^{\circ }$

4. ${85}^{\circ }$

Q.

A quadrilateral has three acute angles, each measuring 75°. Find the measure of the fourth angle.

1. ${225}^{\circ }$

2. ${100}^{\circ }$

3. ${140}^{\circ }$

4. ${135}^{\circ }$

Q.

The three angles of a quadrilateral are 80°, 70° and 70°. The fourth angle is -

1. ${110}^{\circ }$

2. ${100}^{\circ }$

3. ${140}^{\circ }$

4. ${80}^{\circ }$

Q.

In the given figure, PQRS is a rectangle if $\angle RPQ={30}^{\circ }$. Then, the value of (x + y) is:

1. ${90}^{\circ }$

2. ${120}^{\circ }$

3. ${150}^{\circ }$

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

Q.

The three angles of a quadrilateral are 80°, 70° and 120°. The fourth angle is -

1. ${110}^{\circ }$

2. ${100}^{\circ }$

3. ${90}^{\circ }$

4. ${80}^{\circ }$

Q.

If the figure "ABCD" is a parallelogram. Which among the following is/are true?

1. $x={45}^{\circ }$

2. $y={105}^{\circ }$

3. $y={30}^{\circ }$

4. $x={75}^{\circ }$

Q.

Three angles of a quadrilateral are equal. The fourth angle is twice one of the angles.

Find the measure of largest angle.

1. ${144}^{\circ }$

2. ${102}^{\circ }$

3. ${70}^{\circ }$

4. ${72}^{\circ }$

Q. Three angles of a quadrilateral are in the ratio 8 : 2 : 3. If fourth angle is 100°, then the other three angles of the quadrilateral are respectively ___.

1. ${140}^{\circ },{60}^{\circ },{60}^{\circ }$
2. ${80}^{\circ },{110}^{\circ },{70}^{\circ }$
3. ${80}^{\circ },{120}^{\circ },{60}^{\circ }$
4. ${30}^{\circ },{150}^{\circ },{80}^{\circ }$

Q.

The following figure shows a quadrilateral with sides AB and DC parallel to each other.

If $\angle A:\angle D=4:5$

$\angle B=(3x-15{)}^{\circ }and$

$\angle C=(4x+20{)}^{\circ }$

Which of the following options is/are correct ?

1. $\angle A={100}^{\circ }$

   $\angle B={60}^{\circ }$

   $\angle C={120}^{\circ }$

   $\angle D={80}^{\circ }$

2. $\angle A={120}^{\circ }$

   $\angle B={60}^{\circ }$

   $\angle C={120}^{\circ }$

   $\angle D={80}^{\circ }$

3. $\angle A={80}^{\circ }$

   $\angle B={60}^{\circ }$

   $\angle C={120}^{\circ }$

   $\angle D={100}^{\circ }$

4. $\angle A={80}^{\circ }$

   $\angle B={120}^{\circ }$

   $\angle C={60}^{\circ }$

   $\angle D={100}^{\circ }$

Q.

In the given figure, AE and BC are equal and parallel. If the sides AB, CD and DE are equal and $\angle$BAE = 100°, then $\angle$AED is equal to

1. 120°

2. 160°

3. 140°

4. 150°

Q.

If three angles of a quadrlateral are ${76}^{\circ }$, ${104}^{\circ }$ and ${89}^{\circ }$.

Find its fourth angle.

1. ${93}^{\circ }$

2. ${51}^{\circ }$

3. ${91}^{\circ }$

4. ${61}^{\circ }$

Q.

A quadrilateral cannot have more than one right angle.

1. True

2. False

Q.

If two angles of a quadrilateral are ${36}^{\circ }$ and ${72}^{\circ }$ and other two angles are in the ratio 3:4, then the measure of the other two angles are

1. ${100}^{\circ },{152}^{\circ }$

2. ${80}^{\circ },{172}^{\circ }$

3. ${108}^{\circ },{144}^{\circ }$

4. ${120}^{\circ },{132}^{\circ }$

Q.

In a quadrilateral ABCD, $\angle A={90}^{\circ }$, $\angle B=3x$, $\angle C=3x+5$, $\angle D=8x-15$.
Then, the value of $\angle D$ is

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

2. ${20}^{\circ }$

3. ${145}^{\circ }$

4. ${65}^{\circ }$

Q.

In a quadrilateral ABCD, if $\angle A={105}^{\circ }$, $\angle B={75}^{\circ }$
and $\angle C={105}^{\circ }$, then the quadrilateral is a ____

1. Parallelogram

2. Rhombus

3. Trapezium

4. Square

Q.

Three angles of a quadrilateral are in the ratio 8 : 11 : 7. If fourth angle is 100°, then the other three angles of the quadrilateral are respectively ___.

1. ${80}^{\circ },{120}^{\circ },{60}^{\circ }$

2. ${30}^{\circ },{150}^{\circ },{80}^{\circ }$

3. ${80}^{\circ },{110}^{\circ },{70}^{\circ }$

4. ${40}^{\circ },{130}^{\circ },{90}^{\circ }$

Q.

Three angles of a quadrilateral are ${100}^{\circ }$, ${90}^{\circ }$ and ${85}^{\circ }$ .The fourth angle is

1. ${100}^{\circ }$

2. ${85}^{\circ }$

3. ${65}^{\circ }$

4. ${75}^{\circ }$