If angles C and D are vertical angles and are represented by mc = 26x and md = 2x + 10, what is the value of md?

To solve for the value of md, we first need to recognize that vertical angles are equal. This means that:

mc = md

According to the problem, we have:

Setting these two expressions equal to each other, we can write:

26x = 2x + 10

Now, let’s solve for x. First, subtract 2x from both sides:

26x - 2x = 10

This simplifies to:

24x = 10

Next, we divide both sides by 24:

x = 10/24

This reduces to:

x = 5/12

Now that we have the value of x, we can substitute it back into the equation for md:

md = 2x + 10

Substituting the value of x:

md = 2(5/12) + 10

This gives us:

md = 10/12 + 10

Which simplifies to:

md = 5/6 + 10

To combine these, we convert 10 into a fraction with a denominator of 6:

10 = 60/6

So now:

md = 5/6 + 60/6 = 65/6

Therefore, the value of md is:

md = 65/6

In decimal form, this is approximately 10.83.