Enter your answer and show all the steps that you use to solve this problem in the space provided. GI−→ bisects ∠DGH so that m∠DGI is x−3 and m∠IGH is 2x−13 . Find the value of x.
To find the value of x, we can set up an equation using the fact that the angle bisector of an angle divides it into two congruent angles.
Given:
m∠DGI = x - 3 (angle formed by the bisector GI)
m∠IGH = 2x - 13 (angle formed by the bisector GI)
Since GI bisects ∠DGH, it means that m∠DGI = m∠IGH.
Setting these two equations equal to each other:
x - 3 = 2x - 13
Now we can solve for x.
First, let's simplify the equation by subtracting x from both sides:
x - x - 3 = 2x - x - 13
-3 = x - 13
Next, let's isolate x by adding 13 to both sides of the equation:
-3 + 13 = x - 13 + 13
10 = x
Therefore, the value of x is 10.
We are given that GI bisects ∠DGH, which means that ∠DGI is congruent to ∠IGH.
Given that m∠DGI is x-3 and m∠IGH is 2x-13, we can set up an equation to find the value of x.
Since ∠DGI is congruent to ∠IGH, we can set up the following equation:
x - 3 = 2x - 13
To solve for x, we can start by combining like terms:
x - 2x = -13 + 3
Simplifying further:
-x = -10
To isolate x, we divide both sides of the equation by -1:
x = 10
Therefore, the value of x is 10.
To find the value of x in this problem, we need to use the properties of angle bisectors.
In this given scenario, the line GI bisects angle DGH, which means it divides the angle into two equal parts. Let's call the measure of angle DGI as a and the measure of angle IGH as b.
According to the given information, m∠DGI is x-3 and m∠IGH is 2x-13.
Since line GI is an angle bisector, we can say that a is equal to b. Therefore, we have the equation:
a = b
Using the given information:
x - 3 = 2x - 13
Now, let's solve this equation to find the value of x.
1. Start by simplifying the equation:
x - 2x = -13 + 3
-x = -10
2. Multiply both sides of the equation by -1 to isolate x:
x = 10
Therefore, the value of x in this case is 10.