khamblyrosales8
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angle A and angle B are complementary angles. If m angle A = (4x – 28)° And angle B = (4x - 8)°, then find the measure of A.​

Sagot :

hnori22003

Complementary angles have a submission of 90 degrees thus :

[tex]angle \: \: A + angle \: \: B = 90°[/tex]

[tex](4x - 28)° + (4x - 8)° = 90°[/tex]

[tex]4x + 4x - 28 - 8 = 90[/tex]

Collect like terms

[tex]8x - 36 = 90[/tex]

Add both sides 36

[tex]8x - 36 + 36 = 90 + 36[/tex]

[tex]8x = 126[/tex]

Divide both sides by 8

[tex] \frac{8x}{8} = \frac{126}{8} \\ [/tex]

[tex]x = 15.75[/tex]

_____________________________________________

Now let's find the measure of A :

[tex]A = 4x - 28[/tex]

[tex]A = 4 \times (15.75) - 28[/tex]

[tex]A = 63 - 28[/tex]

[tex]A = 35°[/tex]

And we're done...

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