HK¯¯¯¯¯¯¯¯¯

Question

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

Answer 1

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.

Answer 2

What's the answer?

Answer 3

The correct answer is:

x = 12/13

The measure of angle GKJ is 112/13 degrees.

Answer 4

x = 2 m<GKJ = 28 degrees

x = 2 m<GKJ = 32 degrees

x = 5 m<GKJ = 14 degrees

x = 5 m<GKJ = 32 degrees

Answer 5

The answer is:

x = 2 m<GKJ = 28 degrees

Answer 6

<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

Answer 7

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.