Final answer:
The measure of angle KJR is 55°, found by setting up an equation combining the measures of angles RJI and KJR to equal the measure of angle KJI and solving for x.
Step-by-step explanation:
To find the measure of angle KJR, we can use the information given:
m/RJI = 12x - 3
m/KJR = 6x - 5
m/KJI = 172°
Since angles RJI and KJR form a linear pair with angle KJI, their measures add up to m/KJI:
Therefore, m/RJI + m/KJR = m/KJI
Substituting the expressions we have: (12x - 3) + (6x - 5) = 172
Solving the equation: 18x - 8 = 172
Adding 8 to both sides: 18x = 180
Dividing by 18: x = 10
Substitute x into m/KJR: m/KJR = 6(10) - 5 = 60 - 5 = 55°
The measure of angle KJR is 55°.