We can solve this problem using the properties of angles in a quadrilateral.
Since angle 1 is formed by the extended left side and the top side of the quadrilateral, it is an exterior angle. The sum of the interior and exterior angles at a vertex is always 180 degrees. Therefore, angle 1 = 180 - mangle2 = 180 - 31 = 149 degrees.
Similarly, angle 3 is formed by the diagonal and the left side of the quadrilateral. Again, it is an exterior angle. Therefore, angle 3 = 180 - mangle3 = 180 - 72 = 108 degrees.
Therefore, the measure of angle 1 is 149 degrees.
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
113
93
103
1 answer