Question
The folding chair has different settings that change the angles formed by its parts. Suppose mangle2 is 31 and mangle3 is 72. Find mangle1. The diagram is not to scale.
The image of a quadrilateral and its extended sides and diagonals is shown to resemble a folding chair.
· The left side of the quadrilateral is extended up to form the back of the folding chair.
· The top side of the quadrilateral is extended to the right to form the arm rest of the folding chair.
· The right side of the quadrilateral is extended down to form the front leg of the folding chair.
· The diagonal between the upper right vertex of the quadrilateral and the lower left vertex is extended towards the left to form the back leg of the folding chair.
· Angle 1 is formed by the extended left side and the top side of the quadrilateral so that angle 1 is outside of the quadrilateral.
· Two angles are created by the diagonal.
· Angle 2 is formed by the diagonal and the top side of the quadrilateral.
· Angle 3 is formed by the diagonal and the left side of the quadrilateral.
(1 point)
Responses
123
123
113
113
93
93
103
103
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Based on the given information, we know that mangle2 = 31 and mangle3 = 72.
Since mangle2 is formed by the diagonal and the top side of the quadrilateral, we can conclude that angle 1 is equal to mangle2. Therefore, angle 1 = 31.
To find mangle1, we need to use the fact that the sum of the interior angles in a quadrilateral is 360 degrees.
Since angle 2 is formed by the diagonal and the top side of the quadrilateral, and angle 3 is formed by the diagonal and the left side of the quadrilateral, we can write the equation:
mangle2 + mangle3 + mangle1 = 360
Substituting the given values:
31 + 72 + mangle1 = 360
103 + mangle1 = 360
To solve for mangle1, we subtract 103 from both sides:
mangle1 = 360 - 103
mangle1 = 257