Question
Note: 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.
(2 points)
GI−→
bisects ∠DGH
so that m∠DGI
is x−3
and m∠IGH
is 2x−13
. Find the value of x.
(2 points)
Answers
GPT 3.5
To find the value of x, we can use the fact that the bisector of an angle divides it into two congruent angles.
Since GI bisects ∠DGH, we have:
m∠DGI = m∠IGH
We are given that m∠DGI = x - 3 and m∠IGH = 2x - 13, so we can set up the equation:
x - 3 = 2x - 13
To solve for x, we can start by subtracting x from both sides of the equation:
-x + x - 3 = 2x - x - 13
-3 = x - 13
Next, we can add 13 to both sides of the equation:
-3 + 13 = x - 13 + 13
10 = x
Therefore, the value of x is 10.
Since GI bisects ∠DGH, we have:
m∠DGI = m∠IGH
We are given that m∠DGI = x - 3 and m∠IGH = 2x - 13, so we can set up the equation:
x - 3 = 2x - 13
To solve for x, we can start by subtracting x from both sides of the equation:
-x + x - 3 = 2x - x - 13
-3 = x - 13
Next, we can add 13 to both sides of the equation:
-3 + 13 = x - 13 + 13
10 = x
Therefore, the value of x is 10.