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)
Unfortunately, without a diagram or additional information, it is not possible to determine the value of angle 1.
To find mangle1, we need to consider the angles formed by the folding chair.
Since mangle2 is given as 31 and mangle3 is given as 72, we can use the fact that the angles of a quadrilateral add up to 360 degrees.
In this case, the quadrilateral in the diagram forms the four angles, mangle1, mangle2, mangle3, and the fourth angle (let's call it mangle4, since it's not mentioned).
Therefore, we can set up the equation:
mangle1 + mangle2 + mangle3 + mangle4 = 360
Substituting the given values:
mangle1 + 31 + 72 + mangle4 = 360
Combining like terms:
mangle1 + mangle4 + 103 = 360
Now, to solve for mangle1, we need to isolate it on one side of the equation.
Subtracting 103 from both sides:
mangle1 + mangle4 = 257
Thus, we cannot determine the exact value of mangle1 without knowing the value of mangle4.
To find angle 1, we need to use the fact that the sum of the angles in a quadrilateral is 360 degrees.
Given that angle 2 is 31 degrees and angle 3 is 72 degrees, we can find angle 1 as follows:
1. Start with the sum of the angles in a quadrilateral: 360 degrees.
2. Subtract angle 2 and angle 3 from the sum: 360 degrees - 31 degrees - 72 degrees.
3. Calculate the result: 360 degrees - 31 degrees - 72 degrees = 257 degrees.
Therefore, angle 1 measures 257 degrees.