Ray GI bisects angle DGH so that angle DGI is x - 3 and angle IGH is 2x - 13. Find the value of x. Show your work.
Since the angle DGI is bisected, we know that angle DGI is equal to angle IGH. Therefore, we have:
x - 3 = 2x - 13
Simplifying this equation gives:
-x = -10
Multiplying both sides by -1 gives:
x = 10
Therefore, the value of x is 10.
To find the value of x, we can set up an equation based on the information given.
Since Ray GI bisects angle DGH, we know that angle DGI is equal to angle IGH. Therefore, we can set up the equation:
x - 3 = 2x - 13
Let's solve this equation step by step to find the value of x.
Step 1: Simplify the equation by combining like terms:
x - 2x = -13 + 3
Step 2: Simplify further:
-1x = -10
Step 3: Divide both sides of the equation by -1 to solve for x:
x = -10 / -1
Step 4: Simplify the right-hand side of the equation:
x = 10
Therefore, the value of x is 10.
To find the value of x, we can set up an equation based on the information given.
Since Ray GI bisects angle DGH, angle DGI and angle IGH will be equal. Therefore, we can set up the following equation:
x - 3 = 2x - 13
Now, let's solve this equation step by step:
1. Start by subtracting x from both sides of the equation to isolate the constant terms:
x - x - 3 = 2x - x - 13
-3 = x - 13
2. Next, add 13 to both sides of the equation to isolate x:
-3 + 13 = x - 13 + 13
10 = x
Therefore, the value of x is 10.