Question

apply the angle addition postulate
using the diagram and the angle addition
postulate, answer the questions below and check
your understanding.
let ( mangle lkn = 145 ) degrees
find the values in the table
sketch on the diagram and show your thinking.

Explanation:

Step1: Apply Angle Addition Postulate

According to the Angle Addition Postulate, \(m\angle LKN=m\angle LKM + m\angle MKN\). So, \(145=(2x + 10)+(4x-3)\).
Simplify the right - hand side: \(145=2x+10 + 4x-3=6x + 7\).

Step2: Solve for \(x\)

Subtract 7 from both sides of the equation \(145=6x + 7\): \(145-7=6x\), i.e., \(138 = 6x\).
Divide both sides by 6: \(x=\frac{138}{6}=23\).

Step3: Find \(m\angle LKM\)

Substitute \(x = 23\) into the formula for \(m\angle LKM\). \(m\angle LKM=2x+10\).
\(m\angle LKM=2\times23 + 10=46+10=56^{\circ}\).

Step4: Find \(m\angle MKN\)

Substitute \(x = 23\) into the formula for \(m\angle MKN\). \(m\angle MKN=4x-3\).
\(m\angle MKN=4\times23-3=92 - 3=89^{\circ}\).

Answer:

Question	Answer
\(m\angle LKM\)	\(56^{\circ}\)
\(m\angle MKN\)	\(89^{\circ}\)