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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.

Sagot :

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

[tex]\text{ZPMO + KLMN = 180}[/tex]

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

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

Therefore, x = 50.

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

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

Therefore, ZPMO=80 AND ZLMN=100

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