Questions: In the figure, CJ and CR are opposite rays. CP bisects angle NCW and CL bisects angle JCN. If m angle JCN=8r-2 and m angle LCN=3r+15, find m angle JCL.

In the figure, CJ and CR are opposite rays. CP bisects angle NCW and CL bisects angle JCN. If m angle JCN=8r-2 and m angle LCN=3r+15, find m angle JCL.
Transcript text: In the figure, $\overrightarrow{C J}$ and $\overrightarrow{C R}$ are opposite rays. $\overrightarrow{C P}$ bisects $\angle N C W$ and $\overrightarrow{C L}$ bisects $\angle J C N$. If $m \angle J C N=8 r-2$ and $m \angle L C N=3 r+15$, find $m \angle J C L$.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify Given Information
  • \( \overrightarrow{CJ} \) and \( \overrightarrow{CR} \) are opposite rays.
  • \( \overrightarrow{CP} \) bisects \( \angle NCW \).
  • \( \overrightarrow{CL} \) bisects \( \angle JCN \).
  • \( m\angle JCN = 8r - 2 \).
  • \( m\angle LCN = 3r + 15 \).
Step 2: Determine Relationship Between Angles

Since \( \overrightarrow{CL} \) bisects \( \angle JCN \), we have: \[ m\angle JCL = \frac{1}{2} m\angle JCN \]

Step 3: Substitute Given Values

Substitute \( m\angle JCN = 8r - 2 \) into the equation: \[ m\angle JCL = \frac{1}{2} (8r - 2) \]

Step 4: Simplify the Expression

Simplify the expression to find \( m\angle JCL \): \[ m\angle JCL = \frac{1}{2} (8r - 2) \] \[ m\angle JCL = 4r - 1 \]

Final Answer

\[ m\angle JCL = 4r - 1 \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Divide. 36 z^4+32 z^3+9 z^2 / 4 z^2 Simplify your answer as much as possible.
failedAnswered
Which situations are modeled accurately by a periodic 22 function? Select all that apply. the height of a ball tossed in the air as a function of time the vertical height of a point on a rotating wheel as a function of time the height of a swinging pendulum as a function of time the distance from the earth to the moon as a function of time
failedAnswered
26) Which of the following is a food that provides ample amounts of all of the essential amino acids? A) Milk B) Peanut butter C) Navy beans D) Wheat
failedAnswered
Solve by using the quadratic formula. (Enter your ans w=1/w^2 - 4/w + 3 = 0
failedAnswered
Progress 71% Decision Point: How Will Skyrocketing Tuition Affect Moondogs? You've just learned that tuition and fees for the next semester are expected to increase by 15%. How do you think this will impact demand for Moondogs Coffee? Select an option from the choices below and click Submit. - Demand for Moondogs Coffee likely will decrease. - Demand for Moondogs Coffee likely will remain unchanged. - Demand for Moondogs Coffee likely will increase.