Question

What is the measure of EDH? E H F 0 [(5x)/ (4x) D G

Answer 1

Answer:  " 50 " .

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 →  " m∡EDH = 50 ° " .

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Step-by-step explanation:

Note that "5x" and "4x" add up to "90 degrees" ; these are "complementary angles" —meaning that their measurements add up to "90 degrees"—in this case, they form a "right angle" (which is a "90 degree angle".).

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So:   " 5x + 4x = 90 " ; Solve for "5x" ;

                               which is the:  " measure of angle EDH " ;

                                                      [i.e. " m∡EDH "] ;

 → 5x + 4x = 9x ;

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    →  9x = 90 ;

Divide each side of the equation by "9" ;

  to isolate "x" on one side of the equation;

  & to solve for "x" ;

 → 9x / 9 = 90 / 9 ;

to get:

  →  x = 10 ;

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Let's check our answer:

 9x  =? 90 ? ;

→ 9 * 10 =? 90 ? Yes!

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Let us further check our answer:

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"4x + 5x = 90 " ;

→ (4*10) + (5*10) =? 90 ? ;

    → 40 +  50 = ? 90 ? ; Yes!

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Now, since we know that:  " x = 10 " ;

 we can solve for "5x" ; which is the: " m∡EDH " ;

→ m∡EDH =  " 5x "  = " 5* (10) = 50 ° " .

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Hope this is helpful!

Best of luck to you!

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Answer 2

5x + 4x = 90 degrees
9x = 90
x = 10