If you need help solving Quadrilateral questions you can take the help of worksheets present here. Have a glance at the Quadrilateral Worksheet during your practice and take your preparation to the next level. Allot time to practice all the questions available on Printable Worksheet on Quadrilaterals and improve the areas you are lagging. For complete guidance make use of the Quadrilateral Practice Worksheets and clear all your doubts related to them.

We have provided various problems according to the new updated syllabus in the following sections. Solve all of them and check your answers to clear your doubts. For a better understanding of the concept, we have given the step by step explanation for each question.

Check out the below list to know the depth concepts available in Quadrilateral concepts.

### Solved Problems on Quadrilateral Worksheet

1. Fill in the blanks:
(i) A quadrilateral has …………… diagonals.
(ii) A quadrilateral has …………… angles.
(iii) How many sides present in a quadrilateral?
(iv) A quadrilateral has …………… vertices, no three of which are……………….
(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 ……………….

Solution:

(i) Two
(ii) Four
(iii) Four
(iv) four, collinear
(v) Opposite
(vi) 360° (i) How many pairs of opposite sides are there? Name them.
(ii) How many pairs of adjacent sides are there? Name them.
(iii) Also, find how many pairs of adjacent angles are there? Name them.
(iv) How many diagonals are there? Name them.
(v) How many pairs of opposite angles are there? Name them.

Solution:

(i) two; (PQ, SR), (PS, QR)
(ii) four; (PQ, QR), (QR, RS), (RS, SP), (SP, PQ)
(iii) four; (∠P, ∠Q), (∠Q, ∠R), (∠R, ∠S), (∠S, ∠P)
(iv) two; (PR, QS)
(v) two; (∠P, ∠R), (∠Q, ∠S)

3. Prove that the sum of the angles of a quadrilateral is 360°.

Solution:

• ∠PQR, ∠QRS, ∠RSP, and ∠SPQ are the internal angles.
• PR is a diagonal
• PR divides the quadrilateral into two triangles, ∆PQR and ∆PSR

We know that the sum of internal angles of a quadrilateral is 360°, that is, ∠PQR + ∠QRS + ∠RSP + ∠SPQ = 360°.

let’s prove that the sum of all the four angles of a quadrilateral is 360 degrees.
The sum of angles in a triangle is 180°. Now consider triangle PSR,
∠S + ∠SPR + ∠SRP = 180° (Sum of angles in a triangle)
Now consider triangle PQR,
∠Q + ∠QPR + ∠QRP = 180° (Sum of angles in a triangle)
On adding both the equations obtained above we have,
(∠S + ∠SPR + ∠SRP) + (∠Q + ∠QPR + ∠QRP) = 180° + 180°
∠S + (∠SPR + ∠QPR) + (∠QRP + ∠SRP) + ∠Q = 360°
We see that (∠SPR + ∠QPR) = ∠SPQ and (∠QRP + ∠SRP) = ∠QRS.
Replacing them we have, ∠S + ∠SPQ + ∠QRS + ∠Q = 360°
That is, ∠S + ∠P + ∠R + ∠Q = 360°.

Or, the sum of angles of a quadrilateral is 360°. This is the angle sum property of quadrilaterals.

4. The three angles of a quadrilateral are 74°, 56°, and 106°. Find the measure fourth angle?

Solution:

Given that the angles of a quadrilateral are 74°, 56°, and 106°.
The sum of the angles of a quadrilateral is 360°.
The quadrilateral consists of four angles.
Let the fourth angle is x.
x + 74° + 56° + 106° = 360°
x = 360° – 74° – 56° – 106°
x = 124°

The fourth angle is 124°.

5. The angles of a quadrilateral are in the ratio 2 : 4 : 6 : 8. Find the measure of each of these angles?

Solution:

Given that the angles of a quadrilateral are in the ratio 2 : 4 : 6 : 8.
Let the common ratio is x.
2x + 4x + 6x + 8x = 360°
20x = 360°
Divide the above equation by 20 on both sides.
20x/20 = 360°/20
x = 18°
2x = 2 . 18° = 36°
4x = 4 . 18° = 72°
6x = 6 . 18° = 108°
8x = 8 . 18° = 144°
The measure of each of these angles is 36°, 72°, 108°, 144°.

6. A quadrilateral has three acute angles, each measuring 70°. Find the measure of the fourth angle?

Solution:

Given that a quadrilateral has three acute angles, each measuring 70°.
Sum of four angles in any Quadrilateral =360°
Three angles each =70°
70° + 70° + 70° + fourth angle =360°
Fourth angle =360° – 210°
= 150°

Therefore, the fourth angle is 150°.

7. Three angles of a quadrilateral are equal and the measure of the fourth angle is 90°. Find the measure of each of the equal angles?

Solution:

Given that three angles of a quadrilateral are equal and the measure of the fourth angle is 90°.
Let each unknown angle is x. The sum of the angles of a quadrilateral are equal to 360°
x + x + x + 90° = 360°
3x + 90° = 360°
3x = 360° – 90°
3x = 270°
Divide the above equation by 3 on both sides.
3x/3 = 270°/3
x = 90°

The three angles are 90°, 90°, and 90°.

8. Two angles of a quadrilateral measure 65° and 55° respectively. The other two angles equal. Find the measure of each of these equal angles?

Solution:

Given that two angles of a quadrilateral measure 65° and 55° respectively. The other two angles equal.
The sum of the angles of a quadrilateral is equal to 360 degrees.
Let the other two angles be x.
So, x + x + 65° + 55° = 360°
2x + 120° = 360°
2x = 360 – 120° = 240°
x = 240°/2
x = 120 degrees

Hence, the Other two angles are 120 degrees each.

9. Two angles of a quadrilateral measure 45° and 75° respectively. The other two angles equal. Find the measure of each of these equal angles?

Solution:

Given that two angles of a quadrilateral measure 45° and 75° respectively. The other two angles equal.
The sum of the angles of a quadrilateral is equal to 360 degrees.
Let the other two angles be x.
So, x + x + 45° + 75° = 360°
2x + 120° = 360°
2x = 360 – 120° = 240°
x = 240°/2
x = 120 degrees

Hence, the Other two angles are 120 degrees each.