FINDING THE MISSING ANGLE OF A QUADRILATERAL

Find the measure of the indicated angle in each quadrilateral.

Problem 1 :

Solution :

The sum of interior angles of a quadrilateral is 360°

m ∠A + m ∠B + m ∠C + m ∠D = 360°

Here m ∠B = 87°, m ∠C = 112°, and, m ∠D = 92°

m ∠A + 87° + 112° + 92° = 360° 

m ∠A + 291° = 360° 

m ∠A = 360° - 291°

m ∠A = 69°

Problem 2 :

Solution :

The sum of interior angles of a quadrilateral is 360°

m ∠P + m ∠Q + m ∠R + m ∠S = 360°

Here m ∠P = 124°, m ∠R = 68°, and, m ∠S = 71°

124° + m ∠Q + 68° + 71° = 360°

m ∠Q + 263° = 360°

m ∠Q = 360° - 263°

m ∠Q = 97°

Problem 3 :

Solution :

The sum of interior angles of a quadrilateral is 360°

m ∠W + m ∠X + m ∠Y + m ∠Z = 360°

Here m ∠W = 95°, m ∠X = 74°, and, m ∠Z = 46°

95° + 74° + m ∠Y + 46° = 360°

m ∠Y + 215° = 360°

m ∠Y = 360° - 215°

m ∠Y = 145°

Problem 4 :

Solution :

The sum of interior angles of a quadrilateral is 360°

m ∠J + m ∠K + m ∠L + m ∠M = 360°

Here m ∠J = 72°, m ∠L = 49°, and, m ∠M = 89°

72° + m ∠K + 49° + 89° = 360°

m ∠K + 210° = 360°

m ∠K = 360° - 210°

m ∠K = 150°

Problem 5 :

Solution :

m ∠Q + m ∠R + m ∠S + m ∠T = 360°

Here m ∠Q = 98°, m ∠S = 65°, and, m ∠T = 69°

98° + m ∠R + 65° + 69° = 360°

m ∠R + 232° = 360°

m ∠R = 360° - 232°

m ∠R = 128°

Problem 6 :

Solution :

m ∠B + m ∠C + m ∠D + m ∠E = 360°

Here m ∠B = 77°, m ∠D = 86°, and m ∠E = 123°

77° + m ∠C + 86° + 123° = 360°

m ∠C + 286° = 360°

m ∠C = 360° - 286°

m ∠C = 74°

Problem 7 :

Solution :

m ∠U + m ∠V + m ∠W + m ∠X = 360°

Here m ∠U = 67°, m ∠V = 135°, and m ∠W= 105°

67° + 135° + 105° + m ∠X = 360°

m ∠X + 307° = 360°

m ∠X = 360° - 307°

m ∠X = 53°

Problem 8 :

Solution :

m ∠S + m ∠T + m ∠U + m ∠V = 360°

Here m ∠S = 114°, m ∠U = 92°, and, m ∠V= 66°

114° + m ∠T + 92° + 66° = 360°

m ∠T + 272° = 360°

m ∠T = 360° - 272°

m ∠T = 88°

Problem 9 :

Solution :

m ∠E + m ∠F + m ∠G + m ∠H = 360°

Here m ∠E = 146°, m ∠G = 91°, and, m ∠H= 75°

146° + m ∠F + 91° + 75° = 360°

m ∠F + 312° = 360°

m ∠F = 360° - 312°

m ∠F = 48°