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Help, I still don't understand this question!
What is the measure of ∠BAC, ∠ABC, and ∠ACB?

Help I Still Dont Understand This Question What Is The Measure Of BAC ABC And ACB class=

Sagot :

JonHenderson55

The answer is:
   " m∠BAC = 45° ;  m∠ABC, = 64° ; and:  m∠ACB = 70° ."
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Step-by-step explanation:

To find the measure of ∠BCA {"m∠BCA"} :

<BCA is supplementary to " 110 " ; that is, both, or all, of all the measurements that form a "line or line segment";  or any portions thereof,

that can be written in:  "slope-intercept format"

  that is, on Cartesian plane:  " y = mx + b " ;

  in which:  "y" is isolated on the "left-hand side" of the equation; as a single, isolated variable;

  and in which:  "m" is the "slope" (if applicable); and the coefficient to the "x"  value'

  and in which "b" is the "y-intercept"; or more precisely"
    the value of the "y-coordinate"—in: "(x, y)" format —at which:
    " x = 0" ; that is, in the format:  " (0, b)."
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So, to find
m∠BCA :  Subtract our given value, "110" ; from "180" ; as follows:
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  " (180 − 110) = 70" ;
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Now:   Note a triangle, by definition, has 3 (three) sides and 3 (three) angles—and all three (3) angles of a triangle add up to 180°.

So:  We just solved for  m∠ACB ; which is:  70° .

Now shall solve for the value of "x" ; & then find the value of all 3 (three) sides of this triangle

Since all angles within a triangle add up to 180: Let's add them up:
  " 70  +  3x + 20 + 3x = 180 " ;

 Combine the "like terms" on the "left-hand side" of the equation:
  " +3x + 3x = 6x " ;  "+ 70 + 20 = 90 ";
And rewrite the equation:
  "  6x + 90 = 180 " ;

Now, subtract "90" from Each Side of the equation:
  "  6x + 90 − 90 = 180 − 90 " ;
to get:   " 6x = 90 " ;

Now, divide Each side of the equation by "6" ;

  to isolate "x" on one side of the equation ;
    and to solve for "x" :
   " 6x / 6 = 90 / 6 ;

to get:  " x = 15 " ;
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Now, we are asked to find:
1)  " m∠BAC = 3x " ;  Plug in "15" for "x" ; and solve:
                     "3x = 3(15) = 45 " ;
2)  " m∠ABC = "(3x + 20)" ; Plug in "15" for "x"; and solve:
                     "3(15) + 20 = 45 + 20 = 65 " ;
3)  " m∠ACB  = 70 " ; (as per our calculated value);

To check our work—do these 3 (three) numbers add up to 180?

   "45 + 65 + 70 =? 180 ? " ;

   " 110 + 70 = " 180 "? Yes!
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So: The answer is as follows:
   " m∠BAC = 45° ;  m∠ABC, = 64° ; and:  m∠ACB = 70° ."
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Hope this is helpful to you!  Best wishes!

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