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GI−→
bisects ∠DGH
so that m∠DGI
is x−3
and m∠IGH
is 2x−13
. Find the value of x.
(2 points)
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.
To find the value of x, we can use the properties of angles formed by a straight line and the angle bisector.
Given:
m∠DGI = x - 3
m∠IGH = 2x - 13
Since GI bisects ∠DGH, we know that ∠DGI and ∠IGH are adjacent angles and together they form a straight line.
According to the property of angles formed by a straight line, the sum of adjacent angles is equal to 180 degrees.
Therefore, we can write the equation:
m∠DGI + m∠IGH = 180
Substituting the values of m∠DGI and m∠IGH, we get:
(x - 3) + (2x - 13) = 180
Now, we can solve for x:
Combine like terms:
x + 2x - 3 - 13 = 180
3x - 16 = 180
Add 16 to both sides:
3x - 16 + 16 = 180 + 16
3x = 196
Divide both sides by 3:
3x/3 = 196/3
x = 196/3
Therefore, the value of x is 196/3 or approximately 65.333.