a. Write an equation that would help you solve for the missing angle measures. Combine Like Terms! Remember the Triangle Sum Theorem.
b. Solve the equation to find the value of x. Show/Explain all of your steps using inverse operations!
k=12x+1
l=16x-7
j=3x
To find the missing angle measures, we can use the Triangle Sum Theorem, which states that the sum of the angles in a triangle is equal to 180 degrees.
a. The equation to solve for the missing angle measures is:
k + l + j = 180
b. To solve the equation and find the value of x, we substitute the given values for k, l, and j into the equation:
12x + 1 + 16x - 7 + 3x = 180
We combine like terms:
12x + 16x + 3x + 1 - 7 = 180
31x - 6 = 180
Next, we isolate the variable term:
31x = 180 + 6
31x = 186
Finally, we solve for x by dividing both sides of the equation by 31:
x = 186 / 31
x = 6
Therefore, the value of x is 6.
using your value of x from the previous question, solve to find the measure of each angle
m<j
m<k
m<l
To find the measure of each angle, we substitute the value of x (x=6) into the given equations:
1. For angle j:
j = 3x
j = 3(6)
j = 18
Therefore, the measure of angle j is 18 degrees.
2. For angle k:
k = 12x + 1
k = 12(6) + 1
k = 72 + 1
k = 73
Therefore, the measure of angle k is 73 degrees.
3. For angle l:
l = 16x - 7
l = 16(6) - 7
l = 96 - 7
l = 89
Therefore, the measure of angle l is 89 degrees.
To summarize:
- The measure of angle j is 18 degrees.
- The measure of angle k is 73 degrees.
- The measure of angle l is 89 degrees.