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22.02.2021 •
Mathematics
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Ответ:
Explanation:
Note: There are 3 (three) angles in any triangle (by definition).
By definition, all the angles in any triangle add up to 180° .
The problems asks us to find the measure of EACH angle of the triangle.
We can set up an equation; given the information in the problem; to solve for the measure of EACH of the 3 (THREE) angles in the triangle:
→ " x + (x + 90) + (x + 30) = 180 " ;
in which: "x" is the measure of one of the angles;
(specifically, the smallest angle) in the triangle;
"(x + 90)" is the measure of another one of the angles in the triangle;
"(x + 30)" is the measure of another one of the angles in the triangle;
By solving for "x" in the equation; we can solve for the measures of all the angles in the triangle;
→ x + (x + 90) + (x + 30) = 180 ;
x + x + 90 + x + 30 = 180 ;
→ 3x + 120 = 180 ;
Subtract "120" from each side of the equation ;
3x + 120 − 120 = 180 − 120 ;
to get: 3x = 60 ;
Now, divide EACH SIDE of the equation by "3" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
3x = 60 ;
3x / 3 = 60 / 3 ;
x = 20 ;
Now, we have the original equation:
x + (x + 90) + (x + 30) = 180 ;
in which: x = 20° {the smallest angle) ;
"(x + 90)" = "(20 + 90) = 110° ;
"(x + 30)" = "(20 + 30)" = 50° ;
The measurements of the angles are: 110° ; 50° ; 20° .
To check our work:
20 + 110 + 50 =? 180 ?? ; → 130 + 50 =? 180 ?? ; → Yes!