Answer: " 50 " .
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→ " m∡EDH = 50 ° " .
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<u>Step-by-step explanation</u>:
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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