Question

1. the drawing shown below is not drawn to scale. answer each of the following questions based on the diagram. each portion of this problem is independent of the others (does not depend on previous answers). (a) given: ( mangle kjm = 22^circ ) and ( mangle kjl = 84^circ ). find: ( mangle mjl ) (b) given: ( mangle ljm = 145^circ ) and ( mangle kjm = 48^circ ). find: ( mangle ljk )

Explanation:

Part (a)

Step1: Identify angle relationship

$\angle KJL$ is the sum of $\angle KJM$ and $\angle MJL$. So, $m\angle KJL = m\angle KJM + m\angle MJL$.

Step2: Solve for $m\angle MJL$

Rearrange the formula: $m\angle MJL = m\angle KJL - m\angle KJM$. Substitute $m\angle KJL = 84^\circ$ and $m\angle KJM = 22^\circ$. So, $m\angle MJL = 84^\circ - 22^\circ = 62^\circ$.

Step1: Identify angle relationship

$\angle LJM$ is the sum of $\angle LJK$ and $\angle KJM$. So, $m\angle LJM = m\angle LJK + m\angle KJM$.

Step2: Solve for $m\angle LJK$

Rearrange the formula: $m\angle LJK = m\angle LJM - m\angle KJM$. Substitute $m\angle LJM = 145^\circ$ and $m\angle KJM = 48^\circ$. So, $m\angle LJK = 145^\circ - 48^\circ = 97^\circ$.

Answer:

$62^\circ$

Part (b)