Question

Please help me I need the explanation to the question step by step solving

Find the values of x and y.

Answer 1

x = 15; y = 17

Explanation:

A line equals 180 degrees

7x + 7 and 4y form the full line

As such:

7x + 7 + 4y = 180

Another line formation is between 4y and 112

A line equals 180 degrees

4y + 112 = 180

180 = 180 so:

7x + 7 + 4y = 4y + 112

Isolate the variable x

Subtract 4y from both sides

7x + 7 + 4y - 4y = 4y - 4y + 112

7x + 7 = 112

Subtract both sides by 7

7x + 7 - 7 = 112 - 7

7x = 105

Divide both sides by 7

7x ÷ 7 ÷ = 105 ÷ 7

1x = 15

x = 15

If x = 15, plug this new information into the expression with both x and y variables

7(15) + 7 + 4y = 180

Pemdas says multiply first

105 + 7 + 4y = 180

Combine like terms

112 + 4y = 180

Subtract both sides by 112

112 - 112 + 4y = 180 - 112

4y = 68

Divide both sides by 4

4y ÷ 4 = 68 ÷ 4

1y = 17

y = 17

Check work:

7(15) + 7 + 4(17) = 180

Pemdas says multiply first

105 + 7 + 68 = 180

Combine like terms

112 + 68 = 180

180 = 180

This means the variable values are correct

Answer 2

7x + 7= 112
7x - 7= 112-7
7x= 105
(Since it’s multiplication divide and vice versa)
7x/7 = 105/7
X= 15

The two opposite angles need to add up to 180. Since we know one angle is 112 subtract that from 180.

180-112= 68

Now we know what the other angle needs to be so set up the equation.

4y= 68
(Again divide cause it is multiplication)
4y/4= 68/4
Y=17

The answers are:
x=15
y=17