HK¯¯¯¯¯¯¯¯¯
bisects ∠GKJ. ∡HKJ = 5x+4
and ∡HKG = 9x−4
. Solve for x and the m<GKJ
(1 point)
Responses
x = 2 m<GKJ = 28 degrees
x = 2 m
x = 2 m<GKJ = 32 degrees
x = 2 m
x = 5 m<GKJ = 14 degrees
x = 5 m
x = 5 m<GKJ = 32 degrees
The answer is:
x = 2 m<GKJ = 28 degrees
<1 and < 2 are supplementary. If <1 = 2y + 9 and m<2 = 3y-4, what is the measure of <1?(1 point)
Responses
m<1 = 35
m<1 = 13
m<1 = 79
m<1 = 101
Since angle 1 and angle 2 are supplementary, their measures add up to 180 degrees.
We are given that m<1 = 2y + 9 and m<2 = 3y - 4.
Setting up an equation using the given information:
m<1 + m<2 = 180
Substituting the expressions for m<1 and m<2:
(2y + 9) + (3y - 4) = 180
Combining like terms:
5y + 5 = 180
Subtracting 5 from both sides:
5y = 175
Dividing both sides by 5:
y = 35
Now, to find the measure of angle 1:
m<1 = 2y + 9
m<1 = 2(35) + 9
m<1 = 70 + 9
m<1 = 79 degrees
Therefore, the correct measure of angle 1 is:
m<1 = 79 degrees.
To solve for x and the measure of angle GKJ, we need to set up an equation using the given information.
Since angle HKJ is bisected by HK, we know that ∠HKJ = 2∠GKJ.
We are given that ∠HKJ = 5x + 4 and ∠HKG = 9x - 4.
Setting up an equation:
5x + 4 = 2(9x - 4)
Simplifying:
5x + 4 = 18x - 8
Subtracting 5x from both sides:
4 = 13x - 8
Adding 8 to both sides:
12 = 13x
Dividing both sides by 13:
x = 12/13
Now, to find the measure of angle GKJ, we substitute the value of x back into the expression for ∠HKJ:
∠HKJ = 5x + 4
∠HKJ = 5(12/13) + 4
∠HKJ = 60/13 + 52/13
∠HKJ = 112/13
Therefore, the correct solution is:
x = 12/13 and the measure of ∠GKJ is 112/13 degrees.
What's the answer?
The correct answer is:
x = 12/13
The measure of angle GKJ is 112/13 degrees.
x = 2 m<GKJ = 28 degrees
x = 2 m<GKJ = 32 degrees
x = 5 m<GKJ = 14 degrees
x = 5 m<GKJ = 32 degrees