Respuesta :

Step-by-step explanation:

It is a cyclic quadrilateral.

The sum of interior angles of this polygon is equal to 180 degrees.

ATQ,

2x+26y=180

x+13y=90 ....(1)

3x+21y=180

x+7y=60 ....(2)

Subtract equation (1) from (2).

x+7y-(x+13y) = 60-90

x+7y-x-13y=-30

-6y=-30

y = 5

Put the value of y in equation (1

x+13(5) = 90

x+65=90

x = 90-65

x = 25

So,

∠DAB = 26y = 26(5) = 130°

∠ABC = 3x = 3(25) = 75°

∠BCD = 2x = 2(25) = 50°

∠ADC = 21y = 21(5) = 105°

    x = 25, y = 5

    m∠DAB = 26(y) = 180°

    m∠ABC = 3x = 75°

    m∠BCD = 2x = 50°

    m∠ADC = 21y = 105°

Property of a cyclic quadrilateral:

  •   Sum of the opposite angles of a cyclic quadrilateral is 180°.

From the picture attached,

  •   ABCD is a cyclic quadrilateral.
  •   m∠A = 26y°, m∠B = 3x°, m∠C = 2x° and m∠D = 21y°

By using the property of cyclic quadrilateral,

m∠A + m∠C = 180°

26y + 2x = 180

13y + x = 90 --------(1)

m∠B + m∠D = 180°

3x + 21y = 180

x + 7y = 60 --------(2)

Subtract equation (2) from (1),

(13y + x) - (x + 7y) = 90 - 60

6y = 30

y = 5

Substitute y = 5 in equation (1),

13(5) + x = 90

x = 90 - 65

x = 25

Substitute the values of 'x' and 'y' to get the measures of the angles,

m∠DAB = 26(y) = 180°

m∠ABC = 3x = 75°

m∠BCD = 2x = 50°

m∠ADC = 21y = 105°

         Therefore, values of the variables will be,

                            x = 25, y = 5

                            m∠DAB = 26(y) = 180°

                            m∠ABC = 3x = 75°

                            m∠BCD = 2x = 50°

                            m∠ADC = 21y = 105°

Learn more about the cyclic quadrilateral here,

https://brainly.com/question/24142962?referrer=searchResults