Find the value of x.
m∠IHG = 162°
m∠IHK = (4x + 4)°
m∠KHG = (8x + 2)°
Responses
A 19
B 17
C 13
D 15
![Bot](/images/users/3283/128x128.jpeg)
1 year ago
![+Dianna+](/images/users/0/1/128x128.jpeg)
1 year ago
why
![Bot](/images/users/3283/128x128.jpeg)
1 year ago
The sum of angles in a triangle is 180 degrees. So we can use this fact to set up an equation:
m∠IHG + m∠IHK + m∠KHG = 180
Substitute the given angle measures:
162 + (4x + 4) + (8x + 2) = 180
Combine like terms and simplify:
12x + 168 = 180
Subtract 168 from both sides:
12x = 12
Divide both sides by 12:
x = 1
Therefore, the value of x is 1. Plug it back into the given angle measures to check:
m∠IHK = (4x + 4)° = (4 + 4)° = 8°
m∠KHG = (8x + 2)° = (8 + 2)° = 10°
Now we can verify that:
162 + 8 + 10 = 180
So the solution is x = 1, which corresponds to answer choice D) 15.
![Tammy](/images/users/0/1/128x128.jpeg)
1 year ago
The bot assumed that I there was a triangle, no such data is given
m∠IHG = 162°
m∠IHK = (4x + 4)°
m∠KHG = (8x + 2)°
perhaps
4x + 4 + 8x + 2 = 162 ????
12x = 156
x = 13
The question is poorly stated
![Bot](/images/users/3283/128x128.jpeg)
1 year ago
You are correct, I apologize for assuming that there was a triangle. Without any information about the relationship between the angles, we cannot assume that they form a triangle. Your solution is the correct one, and the answer is indeed x=13. Thank you for pointing out the error.
![Explain Bot](/images/users/4931/128x128.jpeg)
7 months ago
To find the value of x, we need to set up an equation based on the given angle measurements and solve for x. Let's do that:
We are given:
m∠IHG = 162°
m∠IHK = (4x + 4)°
m∠KHG = (8x + 2)°
Since the sum of the angles in a triangle is 180°, we can set up the following equation:
m∠IHG + m∠IHK + m∠KHG = 180°
Substituting the given angle measurements, we have:
162° + (4x + 4)° + (8x + 2)° = 180°
Now, we can simplify and solve for x:
162° + 4x + 4 + 8x + 2 = 180°
Combining like terms:
162° + 12x + 6 = 180°
Subtracting 6 from both sides:
162° + 12x = 174°
Subtracting 162 from both sides:
12x = 12°
Dividing both sides by 12:
x = 1°
Therefore, the value of x is 1.