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A, B, C and D are the angles of a Quadrilateral with A= 70°, B= 60°, C= 75°, what are D? Construct and name it.

Mathematics

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Answers

3 parts
a

50∘\mathbf{50^\circ}

b

55∘\mathbf{55^\circ}

c

30∘\mathbf{30^\circ}

Step-by-step solution

9 steps

Part a· 3 steps

Angles on a straight line sum to 180∘180^\circ. These are supplementary angles or *angles on a straight line

  1. Set up the equation for the sum of angles on a straight line.

    A+B+C=180∘A + B + C = 180^\circ

  2. Substitute the given values A=55∘A = 55^\circ and B=75∘B = 75^\circ.

    55∘+75∘+C=180∘55^\circ + 75^\circ + C = 180^\circ

  3. Solve for CC.

    130∘+C=180∘130^\circ + C = 180^\circ C=180∘−130∘C = 180^\circ - 130^\circ C=50∘C = 50^\circ

    The size of CC is 50∘\boxed{\mathbf{50^\circ}}.

Part b

55∘\mathbf{55^\circ}

The sum of angles in a triangle is 180∘180^\circ. These are *angles in a triangle

  1. Set up the equation for the sum of angles in a triangle.

    A+B+C=180∘A + B + C = 180^\circ

  2. Substitute the given values A=90∘A = 90^\circ and B=35∘B = 35^\circ.

    90∘+35∘+C=180∘90^\circ + 35^\circ + C = 180^\circ

  3. Solve for CC.

    125∘+C=180∘125^\circ + C = 180^\circ C=180∘−125∘C = 180^\circ - 125^\circ C=55∘C = 55^\circ

    The size of CC is 55∘\boxed{\mathbf{55^\circ}}.

Part c

30∘\mathbf{30^\circ}

The sum of angles in a quadrilateral is 360∘360^\circ. These are *angles in a quadrilateral

  1. Set up the equation for the sum of angles in a quadrilateral.

    A+B+C+D=360∘A + B + C + D = 360^\circ

  2. Substitute the given values A=150∘A = 150^\circ, B=30∘B = 30^\circ, and C=150∘C = 150^\circ.

    150∘+30∘+150∘+D=360∘150^\circ + 30^\circ + 150^\circ + D = 360^\circ

  3. Solve for DD.

    330∘+D=360∘330^\circ + D = 360^\circ D=360∘−330∘D = 360^\circ - 330^\circ D=30∘D = 30^\circ

    The size of DD is 30∘\boxed{\mathbf{30^\circ}}.

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