if m<ABC=7x-4 and m<CBX=7-x, find the value of x.

Question

Please explain all the steps

Answer 1

I am going to presume that ABX is a straight line. If not, please describe the figure.

In other words, the figure should look something like this:

C

A______/_______X

B

If line segment ABX is not explicitly stated as being a straight line in the problem, you cannot presume it.

By the angle addition postulate,

m∠ABC + m∠CBX = m∠ABX = 180º

since ∠ABX is a straight line.

Given:

m∠ABC = (7x-4)º

m∠CBX = (7-x)º

Using the substitution property of equality,

(7x-4)º + (7-x)º = 180º

For simplicity, let's drop the degree marks while solving this equation.

7x-4 + 7-x = 180

We can use the commutative property of addition (a+b= b+a) while we are combining like terms:

7x + 3 -x = 180

Subtract 3 from both sides:

6x = 177

Now divide both sides of the equation by the coefficient of x:

6x/6 = 177/ 6 = 29.5

x = 29.5

Since x is inside the parentheses above and the degree mark is outside the parenentheses, x is not given a degree mark. You already have it (outside the parentheses).

The next step in such problems is usually to ask for the measures of the angles. You weren't asked for it here. But you should check your answer, and to do that, you can also find the measure of the angles.

m∠ABC = 7x - 4 = 7×(29.5) - 4 = 206.5 - 4 = 202.5º

Note that I put the degree mark back on. Angles are typically measured in degrees, and you should always include the units. (Angles can also be measured in radians, turns, and gradians. Don't worry about these alternative units right now.)

m∠BCX = 7-x = 7-29.5 = -22.5º

Negative angles go clockwise, and positive angles go counter-clockwise. HOWEVER, I think your teacher just made up this problem quickly, without thinking it through. OR, MY DIAGRAM DOES NOT CORRESPOND TO THE ACTUAL PROBLEM.

I am going to finish checking in the hopes that my initial assumption was correct.

202.5º + (-22.5º) = 180º

and that does check out.

If my diagram was not correct, or if you have any questions, please let me know.