Question

date: sep 8, 2025
period:
name:
a. give what is required in each item. (1 point)

1. give 3 line segments in line $overleftrightarrow{ae}$

b. solve the problem. (2 points) the items are independent of each other
2.) if $kn = 96$ and $no = 58$, find $ok$.
3.) if $on = 53$ and $wn = 84$, find $wo$.
b. draw your own figure, then solve the problem. (2 points)
4-5.) suppose $e$ is a point in the interior of $angle rad$. if $mangle rae = 38^circ$ and $mangle dae = 69^circ$, what is $mangle dar$?

Explanation:

Problem 2:

Step1: Understand the segment addition

We know that \( OK = KN + NO \) (by segment addition postulate, as \( K \), \( N \), \( O \) are collinear in that order).

Step2: Substitute the given values

Given \( KN = 96 \) and \( NO = 58 \), so \( OK = 96 + 58 \).

Step3: Calculate the sum

\( 96+58 = 154 \).

Step1: Understand the segment addition

We know that \( WN = WO - ON \) (by segment addition postulate, rearranged to solve for \( WO \), so \( WO = WN + ON \)).

Step2: Substitute the given values

Given \( ON = 53 \) and \( WN = 84 \), so \( WO = 84 + 53 \).

Step3: Calculate the sum

\( 84 + 53=137 \).

Step1: Understand angle addition

Since \( E \) is in the interior of \( \angle RAD \), \( m\angle DAR=m\angle DAE + m\angle RAE \).

Step2: Substitute the given values

Given \( m\angle RAE = 38^\circ \) and \( m\angle DAE = 69^\circ \), so \( m\angle DAR=38^\circ+ 69^\circ \).

Step3: Calculate the sum

\( 38^\circ+69^\circ = 107^\circ \).

Answer:

\( OK = 154 \)

Problem 3: