HK¯¯¯¯¯¯¯¯¯ bisects ∠GKJ. ∡HKJ = 5x+4 and ∡HKG = 9x−4 . Solve for x and the m<GKJ (1 point) Responses x = 5 m<GKJ = 32 degrees x = 5 m x = 2 m<GKJ = 28 degrees x = 2 m x = 5 m<GKJ = 14 degrees x = 5 m x = 2 m<GKJ = 32 degrees
To find the value of x, we need to set up an equation using the fact that the sum of the angles in a triangle is 180 degrees.
Since line HK bisects ∠GKJ, we can use the Angle Bisector Theorem to find the relationship between ∡HKJ and ∡HKG.
Based on the given information, we have:
∡HKJ = 5x + 4
∡HKG = 9x - 4
According to the Angle Bisector Theorem, we can set up the following equation:
∡HKJ / ∡HKG = JK / KG
Substituting the given expressions for the angles, we get:
(5x + 4) / (9x - 4) = JK / KG
But since line HK bisects ∠GKJ, we know that JK=KG, so the equation becomes:
(5x + 4) / (9x - 4) = 1
To solve for x, we can cross-multiply:
5x + 4 = 9x - 4
Simplifying:
4x = 8
Dividing both sides by 4, we get:
x = 2
Now that we have found the value of x, we can substitute it back into one of the given expressions to find the measure of ∡HKJ:
∡HKJ = 5x + 4
∡HKJ = 5(2) + 4
∡HKJ = 14 degrees
Therefore, the correct answer is:
x = 2
∡HKJ = 14 degrees
To solve for x and the measure of ∠GKJ, we can use the properties of angle bisectors.
Since HK bisects ∠GKJ, we can set up the following equation:
∠HKJ = ∠HKG
Given that ∠HKJ = 5x + 4 and ∠HKG = 9x - 4, we can equate them:
5x + 4 = 9x - 4
Simplifying the equation:
4x = 8
Divide both sides of the equation by 4:
x = 2
Now, with the value of x, we can find the measure of ∠GKJ.
∠GKJ = 5x + 4
Substituting x = 2:
∠GKJ = 5(2) + 4
∠GKJ = 10 + 4
∠GKJ = 14 degrees
Hence, the solution is:
x = 2
m< GKJ = 14 degrees
To solve for x and the measure of angle GKJ, we need to set up an equation based on the given information.
According to the problem, HK bisects angle GKJ. This means that the measure of angle HKJ is equal to the measure of angle HKG. So we can set up an equation:
∠HKJ = ∠HKG
Using the given measures of the angles:
5x + 4 = 9x - 4
Now we can solve for x.
First, let's isolate the x term on one side of the equation:
4 + 4 = 9x - 5x
8 = 4x
Now, divide both sides of the equation by 4 to solve for x:
8/4 = 4x/4
2 = x
Therefore, x equals 2.
Now that we have found the value of x, we can substitute it back into one of the angle measures to find the measure of angle GKJ.
Using ∠HKJ = 5x + 4:
∠HKJ = 5(2) + 4
∠HKJ = 10 + 4
∠HKJ = 14
So, the measure of angle GKJ is 14 degrees.
Therefore, the correct answer is:
x = 2 and m<GKJ = 14 degrees.