Quadrilateral Worksheet

In math practice test on quadrilateral worksheet we will practice different types of questions in quadrilateral. Students can practice the questions of quadrilateral worksheet before the examinations to get more confident.

Quadrilateral Worksheet:

1. 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 ……………… . 

2. In the adjoining figure, ABCD is a quadrilateral. 

  (i) How many pairs of adjacent sides are there? Name them.

  (ii) How many pairs of opposite sides are there? Name them.

  (iii) How many pairs of adjacent angles are there? Name them.

  (iv) How many pairs of opposite angles are there? Name them.

  (v) How many diagonals are there? Name them.

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

4. The three angles of a quadrilateral are 76°, 54° and 108°. Find the measure fourth angle.

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

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

7. Three angles of a quadrilateral are equal and the measure of the fourth angle is 120°. Find the measure of each of the equal angles.

8. Two angles of a quadrilateral measure 85° and 75° respectively. The other two angles equal. Find the measure of each of these equal angles.

9. In the adjacent figure, the bisectors of ∠A and ∠B meet in a point P.
If ∠C = 1000 and ∠D = 60°, find the measure of ∠APB.

Hint: 60° + 100° + ∠A + ∠B = 360°

⇒ ∠A + ∠B = 200°

⇒ ¹/₂ ∠A + ¹/₂ ∠B = 100°

⇒ ∠BAP + ∠ABP = 100°

But, ∠BAP + ∠ABP + ∠APB = 180° (why?)

Now, find ∠APB.

Answers for quadrilateral worksheet are given below to check the exact answers of the above questions.

Answers:

1. (i) four

(ii) four

(iii) four, collinear

(iv) two

(v) opposite

(vi) 360°

2. (i) four; (AB, BC), (BC, CD), (CD, DA), (DA, AB)

(ii) two; (AB, DC), (AD, BC)

(iii) four; (∠A, ∠B), (∠B, ∠C), (∠C, ∠D), (∠D, ∠A)

(iv) two; (∠A, ∠C), (∠B, ∠D)

(v) two; (AC, BD)

4. 122°

5. 45o, 75o, 105°, 135°

6. 135°

7. 80o

8. 100°

9. 80°

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