the four interior angles of a quadliteral are 3x + 80° , 5x + 10° , 3x - 20° and 4x -10° . Calculate each interior angle of the quadliteral.
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the four interior angles of a quadliteral are 3x + 80° , 5x + 10° , 3x - 20° and 4x -10° . Calculate each interior angle of the quadliteral.
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Answer:
The sum of the interior angles of a quadrilateral is 360 degrees.
Therefore,
(3x + 80°) + (5x + 10°) + (3x - 20°) + (4x -10°) = 360°
Simplifying and solving for x:
15x + 60° = 360°
15x = 300°
x = 20°
Now that we know x, we can find each interior angle of the quadrilateral:
3x + 80° = 3(20) + 80° = 60° + 80° = 140°
5x + 10° = 5(20) + 10° = 100° + 10° = 110°
3x - 20° = 3(20) - 20° = 60° - 20° = 40°
4x - 10° = 4(20) - 10° = 80° - 10° = 70°
Therefore, the interior angles of the quadrilateral are: 140°, 110°, 40°, and 70°.
Step-by-step explanation:
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