If m∠FCG = 9x + 3 and m∠GCB = 13x – 9, find m∠GCB
To find the measure of angle GCB (m∠GCB), we need to use the given information about angles FCG and GCB.
Step 1: Set up an equation using the given angle measurements.
m∠FCG = 9x + 3
m∠GCB = 13x - 9
Step 2: Set the two angles equal to each other.
9x + 3 = 13x - 9
Step 3: Solve for x.
9x - 13x = -9 - 3
-4x = -12
x = 3
Step 4: Substitute the value of x back into the equation to find the measure of angle GCB.
m∠GCB = 13(3) - 9
m∠GCB = 39 - 9
m∠GCB = 30
Therefore, the measure of angle GCB is 30 degrees.
To find the measure of ∠GCB, we need to know the value of x.
Given that:
m∠FCG = 9x + 3
m∠GCB = 13x - 9
We can set these two angles equal to each other since they share the common side, CG.
9x + 3 = 13x - 9
To solve for x, we can simplify the equation as follows:
9x + 3 = 13x - 9
9x - 13x = -9 - 3
-4x = -12
x = (-12) / (-4)
x = 3
Now that we know the value of x, we can substitute it back into either equation to find the measure of ∠GCB.
Using m∠GCB = 13x - 9:
m∠GCB = 13(3) - 9
m∠GCB = 39 - 9
m∠GCB = 30
Therefore, the measure of ∠GCB is 30 degrees.