Question

In quadrilateral ABCD angle b = 90 degree , angle c - angle d = 60 degree and angle a - angle c - angle d = 10 , find angle a , angle c , angle d​

Answer 1

In quadrilateral ABCD interior angle are $\mathbf{\angle A=140^{\circ},\angle B=90^{\circ},\angle C=95^{\circ} and \angle D=35^{\circ}}$

Step-by-step explanation:

1. Given data about quadrilateral

  $\mathbf{\angle B=90^{\circ}}$       ...1)

  $\mathbf{\angle C - \angle D=60^{\circ}}$    ...2)

  $\mathbf{\angle A-\angle C - \angle D=10^{\circ}}$    ...3)

2. In quadrilateral sum of all interior angle

   $\mathbf{\angle A+\angle B+\angle C+\angle D=360^{\circ}}$     ...4)

3. Adding equation 3) and Equation, we get

  $\mathbf{2\angle A+\angle B=360^{\circ}+10^{\circ}}$

  $\mathbf{2\angle A+\angle B=370^{\circ}}$       ...5)

4. From equation 1) and equation 5)

   $\mathbf{2\angle A+\angle B=370^{\circ}}$

   $\mathbf{2\angle A+90^{\circ}=370^{\circ}}$

   So

   $\mathbf{\angle A=140^{\circ}}$        ...6)

5. From  equation 6) and equation 3)

   $\mathbf{\angle A-\angle C - \angle D=10^{\circ}}$

   

   $\mathbf{140^{\circ}-\angle C - \angle D=10^{\circ}}$

   So

   $\mathbf{\angle C + \angle D=130^{\circ}}$        ...7)

6.  From equation 7) and equation 2)

     $\mathbf{\angle C + \angle D=130^{\circ}}$

     $\mathbf{\angle C - \angle D=60^{\circ}}$

     On Adding and subtracting above both equation we get

     $\mathbf{\angle C =95^{\circ}}$   and $\mathbf{\angle D=35^{\circ}}$

     

Answer 2

Answer:

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In quadrilateral ABCD interior angle are  

Step-by-step explanation:

1. Given data about quadrilateral

        ...1)

     ...2)

     ...3)

2. In quadrilateral sum of all interior angle

       ...4)

3. Adding equation 3) and Equation, we get

 

        ...5)

4. From equation 1) and equation 5)

   

   

  So

          ...6)

5. From  equation 6) and equation 3)

   

   

   

  So

          ...7)

6.  From equation 7) and equation 2)

     

     

    On Adding and subtracting above both equation we get

       and