Question

ZPMO and KLMN form a linear pair. The measure of ZPMO is (X + 30). The measure of ZLMN is (2x) 1. What is the value of x? (Write a number only.) 2. The measure of LMN is (Write a number only.) 1 2.

Answer 1

Given that ZPMO and KLMN form a linear pair, we have:

`\text{ZPMO + KLMN = 180}`

Since ZPMO=X+30 and ZLMN=2X, then:

`\begin{gathered} (x+30)+(2x)=180 \\ \Rightarrow3x=180-30 \\ \Rightarrow3x=150 \\ \Rightarrow x=(150)/(3)=50 \\ x=50 \end{gathered}`

Therefore, x = 50.

Finally, to find the measure of both angles, we just substitute x=50:

`\begin{gathered} x=50 \\ \text{ZPMO}=X+30 \\ \Rightarrow ZPMO=50+30=80 \\ \text{ZLMN}=2x \\ \Rightarrow ZLMN=2\cdot50=100 \end{gathered}`

Therefore, ZPMO=80 AND ZLMN=100