PROBLEMS ON EXTERIOR ANGLES OF A QUADRILATERAL

Sum of exterior angle of quadrilateral is 360°.

∠A + ∠B + ∠C + ∠D = 360

Find the unknown values in the following :

Problem 1 :

Solution :

∠CDA = 180 - x,  ∠CDE = x

Sum of interior angles of a quadrilateral = 360

118 + 71 + 97 + 180 - x = 360

466 - x = 360

x = 466-360

x = 106

Problem 2 :

Solution :

∠BCE = 100, ∠CEA = 180 - x

Sum of interior angles of a quadrilateral = 360

52 + 141 + 100 + 180 - x = 360

473 - x = 360

Subtracting 473 on both sides.

-x = 360 - 473

-x = -113

x = 113

Problem 3 :

Solution :

∠DAB = 90

∠ADC = 180-132 ==> 48

Sum of interior angles = 360

90 + x + 145 + 48 = 360

283 + x = 360

Subtracting 283 on both sides.

x = 360 - 283

x = 77

Problem 4 :

Solution :

Reflexive angle of ∠C = ∠BCD

Sum of interior angle = 360

180 - x + 51 + 85 + 148 = 360

464 - x = 360

Subtracting 464 on both sides.

-x = 360 - 464

-x = -104

x = 104

Problem 5 :

Solution :

Reflexive of ∠B = 360 - 341

∠ABD = 19

Reflexive of ∠C = 360 - 335

∠DCA = 25

Reflexive of ∠A = 360 - 300

∠CAB = 60

Reflexive of ∠BDC = 360 - x

Sum of the interior angles = 360

19 + 25 + 60 + 360 - x = 360

464 - x = 360

Subtracting 464 on both sides.

x = 464 - 360

x = 104

Problem 6 :

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

Solution :

m∠G + m∠F + m∠H + m∠HEF = 360

80 + 110 + 74 + m∠HEF = 360

264 + m∠HEF = 360

Subtracting 264 on both sides.

m∠HEF = 360 - 264

m∠HEF = 96

m∠HEF + m∠1 = 180

96 + m∠1 = 180

Subtracting 96 on both sides.

m∠1 = 180 - 96

m∠1 = 94