Question

I need help with this question please help

Question 1 options:

70


180


67


40


140


143

Answer 1

Explanation:

By definition of a parallelogram, we know that the opposite angles are equal.

Thus, x+73=3x-7.

We can further use algebra and subtract by 3x and 73 on both sides.

We now have -2x=-80.

If we divide both sides by -2, then we get x=40.

We can plug x=40 back into 3x-7 and x+73, and we get 113 for both angles, which of course makes sense because they should be equal.

By definition of a parallelogram, we know that the angles of a parallelogram add up to 360, and that angle DAB = angle BCD = z-3.

This means that 113+113+z-3+z-3=360.

Combining like terms, we get 220+2z=360.

We can use algebra again, and subtract both sides by 220, getting 2z=140.

Dividing both sides by 2, we get z=70.

Because angle DAB=z-3, and z=70, we can plug in 70 for z, producing the result of angle DAB=67.

Answer 2

Explanation:

1. in a parallelogram the opposite angles are equal.

so,

3x - 7 = x + 73

and

angle DAB = angle DCB = z - 3

3x - 7 = x + 73

2x - 7 = 73

2x = 80

x = 40

angle ADC = angle ABC = x + 73 = 40 + 73 = 113°

to get to z we need also to remember, as a quadrilateral shape the sum of all inner angles of a parallelogram is 360°.

so,

2×113 + 2×(z - 3) = 360

226 + 2z - 6 = 360

220 + 2z = 360

2z = 140

z = 70

angle DAB = angle DCB = z - 3 = 70 - 3 = 67°