INTERIOR AND EXTERIOR ANGLES OF QUADRILATERALS WORKSHEET

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Find the value of x in the following quadrilaterals :

Problem 1 :

Problem 2 :

Problem 3 :

Problem 4 :

Problem 5 :

Problem 6 :

Find the values of a and b.

Solution

Problem 7 :

Solution

Problem 8 :

Solution

Problem 9 :

find the measures of the numbered angles in rhombus DEFG.

Problem 10 :

Problem 11 :

Problem 12 :

Problem 13 :

The measures of the interior angles of a quadrilateral are x°, 3x°, 5x°, and 7x°. Find the measures of all the interior angles.

Solution

Problem 14 :

Find the values of x and y that make the quadrilateral a parallelogram

Solution

Answer Key

1) x = 65

2) x = 93

3) x = 35

4) x = 40

5) x = 50

6) a = 65 and b = 89

7) m = 60 and n = 65

8) a = 70

9) ∠4 = ∠1 = 27, ∠6 = 63, ∠5 = 63, ∠3 = 90, ∠2 = 27

10) ∠1 = 90, ∠2 = 42, ∠3 = 42, ∠5 = 48, ∠4 = 48

11) ∠1 = 37, ∠4 = ∠3 = 37 = ∠2, ∠5 = 106, ∠4 = 37

12) ∠1 = 54, ∠5 = 54, ∠2 = 72, ∠3 = 72 and ∠4 = 72

13) the required interior angles are 22.5, 67.5, 112.5 and 157.5

14) the value of x is 25 and y is 25.

Find the unknown values in the following :

Problem 1 :

Problem 2 :

Problem 3 :

Problem 4 :

Problem 5 :

Problem 6 :

Find m∠1 if m∠G = 80, m∠F = 110 and. m∠H = 74.

Solution

Problem 7 :

In the given figure, ABCD is a parallelogram. Find the values of x, y, z and p.

Solution

Problem 8 :

Find x + y + z + w in the given figure.

Solution

Problem 9 :

If three angles of a quadrilateral are each equal to 75°, the fourth angle is :

(a) 150° (b) 135° (c) 45° (d) 75°

Solution

Problem 10 :

What is the maximum number of obtuse angles that a quadrilateral can have ?

(a) 1 (b) 2 (c) 3 (d) 4

Solution

Problem 11 :

In the figure, ABCD is a square. If ∠DPC = 80°, then find .

Solution

Problem 12 :

The angle of ∠M, ∠N, ∠O and ∠P of a trapezium MNOP intersect at points W and X respectively. If ∠MPX = 50, ∠NOX = 70, find the measure of the angles a, b, c and d

Solution

Answer Key

1) x = 106

2) x = 113

3) x = 77

4) x = 104

5) x = 104

6) m∠1 = 94

y = 100
p = 80
x = 100
z = 70

8) the value of x + y + z + w is 360.

9) x = 135

10) A quadrilateral can have a maximum of three obtuse angles because the sum of all interior angles in any quadrilateral is 360°, and if three angles were obtuse (greater than 90°), their sum alone would be over 270°, leaving room for the fourth angle to be acute (less than 90°) to total 360°

11) x = 125

12) a = 60, b = 120, c = 90, d = 90

Find the unknown angles of a quadrilateral.

Problem 1 :