The answer is: 53° .
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Explanation:
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All three angles in ANY triangle add up to: 180° .
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We are given the measurements of two of the angles in a triangle,
50, and 27. We know that the sum of the three (3) angles = 180.
We want the measurement ofthe unknown angle, which we will represent with the variable, "x".
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Method 1:
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So, 50 + 27 + x = 180 ;
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→ Subtract "50" and subtract "27" from EACH SIDE of the equation;
to isolate "x" on one side of our equation; and to solve for "x" ;
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→ 50 + 27 + x − 50 − 27 = 180 − 50 − 27 ;
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→ to get: x = 53° .
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Method 2:
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So, 50 + 27 + x = 180 ;
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→ Add: "50 + 27" ; to get, "77" ;
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→ Rewrite as: 77 + x = 180 ;
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→ Now, subtract "77" from EACH SIDE of the equation;
to isolate "x" on one side of our equation; and to solve for "x" ;
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→ 77 + x − 77 = 180 − 77 ;
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→ to get: x = 53° .
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Method 3:
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→ 180 − (50 + 27) = x ; Solve for "x"
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→ 50 + 27 = 77 ;
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→ Rewrite the equation, substituting "77" in lieu of "(50 + 27)" ;
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→ 180 − 77 = x ; → 53 = x ; ↔ x = 53° .
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Method 4:
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180 − (50 + 77) = x ; solve for 'x";
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→ Note the "distributive property of multiplication:
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a*(b + c) = ab + ac ; AND:
a*(b − c) = ab − ac ;
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→ So, we have: 180 − (50 + 77) = x ;
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Treat this as: " 180 − 1(50 + 77)" ;
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→ Note, the coefficient "1" is implied; and makes since, since any value, multiplied by "1" equals that same value.
→ We treat this number as "-1", since there is a subtraction sign; so, let us consider the expression: " -1(50 + 77) "
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→ -1(50 + 77) = (-1*50) + (-1*77) ;
→ -50 + (-77) = -50 -77 = -127 ;
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→So rewrite the equation: Bring down the "180";
& bring down the "-127" and the: "= x " ;
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→ 180 − 127 = x ; to get: → 53 = x ; ↔ x = 53° .
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