4. Isosceles trapezoid POST with OS || PT If m2O=(10x+20)' and mzP=8x-
2), what is x?

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4. Isosceles trapezoid POST with OS || PT If m2O=(10x+20)' and mzP=8x-
2), what is x?

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Chirilugo Chirilugo · Answer 1

[tex]\bold {PROBLEM:}[/tex]

Isosceles trapezoid POST with OS || PT. If m∠O=(10x+20)° and m∠P=(8x-2)°, what is x?

[tex]\bold {SOLUTION:}[/tex]

Given that OS || PT, ∠O and ∠P are same-side consecutive angles so they are supplementary, thus,

[tex] \large \tt m \angle O + m \angle P = 180° \\ \\ \large \tt (10x + 20) + (8x - 2) = 180 \\ \\ \large \tt 18x + 18 = 180 \\ \\ \large \tt 18x = 180 - 18 \\ \\ \large \tt 18x = 162 \\ \\ \large \tt \frac{18x}{18} = \frac{162}{18} \\ \\ \large \red{ \boxed{ \tt x = 9}} [/tex]

[tex]\\ \\[/tex]

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