Angle Sum Property of a Quadrilateral

Q. ABCD is a kite. If $\angle DAB$ is two times $\angle ADC$, find the value of $\angle ABC$ in terms of $\angle ADC$.

1. $\angle ABC={180}^{\circ }-4\angle ADC$
2. $\angle ABC={360}^{\circ }+4\angle ADC$
3. $\angle ABC={360}^{\circ }-4\angle ADC$
4. $\angle ABC={180}^{\circ }+4\angle ADC$

Q.

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

Q. If the exterior angles of a pentagon are $k^{\circ },k^{\circ },2k^{\circ },2k^{\circ },\text{and}3k^{\circ }$, then find the value of $k$.

1. 4
2. 10
3. 40
4. 60

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.

Q. Find the sizes of the angles of a Parallelogram if one angle is 20° less than twice the smallest angle

Q.

If the angles of a quadrilateral are in the ratio 3:4:6:7, then the quadrilateral is a___.

1. Angles A & B

2. Angles B & C

3. Angles A & C

4. Angles C & D

Q. In the given figure, ABCD is a quadrilateral and AO and DO are bisectors of $\angle Aand\angle D$. The value of 'x ' is

1. ${70}^{\circ }$
2. ${85}^{\circ }$
3. ${120}^{\circ }$
4. ${95}^{\circ }$

Q. ABCD is a kite. If $\angle DAB$ is two times $\angle ADC$, find the value of $\angle ABC$ in terms of $\angle ADC$.

Q.
Question 161
Find the values of x and y in the following parallelogram.

Q.

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

1. 
2. 
3. 
4. 

Q. Question 12
What is the maximum number of obtuse angles that a quadrilateral can have?
a) 1
b) 2
c) 3
d) 4

Q.

Two angles of a quadrilateral measure ${85}^0$ and ${75}^0$ respectively. The other two angles are equal. Find the measure of each of these equal angles.

Q.

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.

Q. Question 7 (b)
(b) Find x+y+z+w

Q. If a quadrilateral has three acute angles each measure ${75}^{\circ }$ find the measure of the fourth angle.

1. 125 degrees
2. 135 degrees
3. 115 degrees
4. 235 degrees.

Q.

From the given figure find $\angle DBC$

1. ${30}^{\circ }$

2. ${110}^{\circ }$

3. ${60}^{\circ }$

4. ${90}^{\circ }$

Q. Question 1
Find x in the following figures:

Q. Question 16
If two adjacent angles of a parallelogram are $(5x-5{)}^{\circ }$ and $(10x+35{)}^{\circ }$, then the ratio of these angles is ___________.
a) 1 : 3
b) 2 : 3
c) 1 : 4
d) 1 : 2

Q. Three angles of a quadrilateral measure ${37}^{\circ }$, ${130}^{\circ }$ and ${53}^{\circ }$. Then the fourth angle is

1. ${40}^{\circ }$
2. ${50}^{\circ }$
3. ${90}^{\circ }$
4. ${140}^{\circ }$

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

Q.

A quadrilateral has three acute angles, wach measuring ${75}^0$. Find the measure of the fourth angle.

Q. Question 138
The adjacent angles of a parallelogram are $(2x-4{)}^{\circ }$ and $(3x-1{)}^{\circ }$. Find the measures of all angles of the parallelogram.

Q. ntABCD is a rhombus in which angle A = 60 degree. Find the ratio AC : BD.n

Q. In parallelogram ABCD, $\angle$A is 3 times $\angle$B. Find all the angles of the parallelogram. In the same parallelogram of AB = 5x -7 and CD = 3x + 1; find the length of CD.

Q. Complete the following, so as to make a true statement :

$ix)$ The sum of the angles of a quadrilateral is right angles.

Q.

The measure of two adjacent angles of a parallelogram in the ratio of $3:2$ find the measure of each angel.

Q.

If opposite angles in a parallelogram are 110 degrees each, what are the other 2 angles?

1. 70 Degrees Each

2. 220 Degrees Each

3. 140 Degrees Each

4. 110 Degrees Each

Q.

What is the sum of either pair of opposite angles of a cyclic quadrilateral?

1. 90°

2. 180°

3. 360°

4. 45°

Q.

In the given figure, sides AB and CD of the quadrilateral ABCD are produced. Find the value of \(x\).

Q. Find the measure of angle $x$ in the following figure​.