Three angles have measures that add to 180 degrees. They have the following angle measures m ABC=(x+15) degrees, m BCD=(x+48), and m DCE= 13 degrees. what is the value of BCD?

Answer 1

To find the value of BCD, we need to set up an equation using the fact that the sum of the three angles is 180 degrees.

The measure of angle ABC is given as (x+15) degrees.
The measure of angle BCD is given as (x+48) degrees.
The measure of angle DCE is given as 13 degrees.

Adding up all three angles, we get:

(x+15) + (x+48) + 13 = 180.

Combining like terms, we have:

2x + 76 = 180.

Subtracting 76 from both sides, we get:

2x = 104.

Dividing both sides by 2, we find:

x = 52.

Now that we know the value of x, we can substitute it back into the expression for BCD:

(x+48) = (52+48) = 100.

Therefore, the value of BCD is 100 degrees.