Question

Solve for x and y. Show your work and include an explanation of what you used (definitions and theorems) to solve the problem.

Answer 1

The value of x and y in the diagram given in the question is:

• x = 5
• y = 10

How to calculate the value of x and y?

The value of x and y in the diagram can be calculated as follow:

For y:

The diagram given in the question is an isosceles triangle and as such,

73 = 8y - 7

Collect like terms

73 + 7 = 8y

80 = 8y

Divide both side by 8

y = 80 / 8

y = 10

For x:

The sum of angles in a triangle is equal to 180, Thus, we have:

73 + (8y - 7) + (6x + 4) = 180

But,

y = 8

Thus, we have

73 + 8(10) - 7 + 6x + 4 = 180

73 + 80 - 7 + 6x + 4 = 180

150 + 6x = 180

6x = 180 - 150

6x = 30

x = 30 / 6

x = 5

In conclusion, we have x and y to be:

• x = 5
• y = 10