Seudónimo Seudónimo

22-04-2022
Mathematics

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If the complement of the angle a is B and the supplement of the angle B is 4a, then find the measure of the angle B

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22-04-2022

[tex] \alpha + \beta = 90[/tex]

[tex] \beta + 4 \alpha = 180[/tex]

Multiply the upper system by -1:

[tex] - \alpha - \beta = - 90[/tex]

[tex] \beta + 4 \alpha = 180[/tex]

Add the systems:

[tex]3 \alpha = 90[/tex]

[tex] \alpha = 30[/tex]

[tex] \beta = 90 - \alpha = 90 - 30 = 60[/tex]

[tex]( \alpha = 30) < = > ( \beta = 60)[/tex]

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