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Sagot :
Answer:
smallest angle = 84°
2nd angle = 88°
third angle = 92°
Explanation:Given:
The interior angles of a quadrilateral form an arithmetic sequence
The largest angle = 96°
To find:
the other angles
The sum of the interior angles of a quadrilateral = 360°
For an arithmetic sequence, there is a common difference
let the common difference = d
let the sequence:
a, a + d, a + 2d, a + 3d
a = first angle
a + 3d = last angle = 96°
if a + 3d = 96
a + 2d = 96 - common difference
a + 2d = 96 - d
a + d = 96 - 2d
a = 96 - 3d
The sequence:
96-3d, 96-2d, 96-d, 96
Sum of the angles in the interior:
[tex]\begin{gathered} 96-3d\text{ + 96-2d + 96 - d + 96 = 360\degree} \\ \\ 96\text{ + 96 + 96 + 96 + -3d - 2d - d = 360} \\ \\ 384\text{ - 6d = 360} \end{gathered}[/tex][tex]\begin{gathered} add\text{ 6 to both sides:} \\ 384\text{ - 6d + 6d = 360 + 6d} \\ \\ 384\text{ - 360 = 6d} \\ \\ 24\text{ = 6d} \\ \\ divide\text{ both sides by 6:} \\ d\text{ = 24/6 = 4} \end{gathered}[/tex]substitute for d, to get the angle measure
[tex]\begin{gathered} 1st\text{ angle = smallest angle = 96 - 3d} \\ smallest\text{ angle = 96-3\lparen4\rparen} \\ smallest\text{ angle = 96-3\lparen4\rparen= 84\degree} \\ \\ Next\text{ angle = 96 - 2d } \\ Next\text{ angle = 96 - 2\lparen4\rparen} \\ Next\text{ angle = 88\degree} \\ \\ Third\text{ angle = 96 - d} \\ Third\text{ angle = 96 - 4} \\ Third\text{ angle = 92\degree} \end{gathered}[/tex]
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