Question

Help with 8th-grade middle school math show work

Answer 1

What they said I believe is correct

Answer 2

Answer:

So for the triangle, we have x = 25 and the angles 45-75-60.

So for the quadrilateral, we have x = 75 and the angles 70-110-75-105.

Step-by-step explanation:

For each of these problems, we can simply add the expressions of the angles given matched to the sum of the angles for the shape given below.  Once we do this, we can solve for x, and then state the given measures of each angle of the shapes.

For the triangle:

60 + ( x + 20 ) + 3x = 180

60 + x + 20 + 3x = 180

60 + 20 + x + 3x = 180

80 + x ( 1 + 3 ) = 180

80 + x ( 4 ) = 180

80 + 4x = 180

4x = 100

x = 25

We have the given angles:

x + 20 ==> 25 + 20 ==> 45

3x ==> 3 (25) ==> 75

60

So for the triangle, we have the angles 45-75-60.

For the quadrilateral:

( x - 5 ) + ( x + 35 ) + x + 1.4x = 360

x - 5 + x + 35 + x + 1.4x = 360

35 - 5 + x + x + x + 1.4x = 360

30 + x ( 1 + 1 + 1 + 1.4 ) = 360

30 + x ( 4.4 ) = 360

30 + 4.4x = 360

4.4x = 330

x = 75

So, we have the given angles:

x - 5 ==> 75 - 5 ==> 70

x + 35 ==> 75 + 35 ==> 110

x ==> 75

1.4x ==> 1.4(75) ==> 105

So for the quadrilateral, we have the angles 70-110-75-105.

Cheers.