Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Drawings not to scale
On Quadrilateral A B C D, side A B measures 10 units and side A D measures 6 units. Angle D measures 86 degrees and Angle C measures 41 degrees. On Quadrilateral J K L M, side K L measures 16 units and side L M measures 17 units. Angle J measures 133 degrees.
The two figures above are congruent. Find the measure of the angle that isn't labeled on either figure.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Drawings not to scale
On Quadrilateral A B C D, side A B measures 10 units and side A D measures 6 units. Angle D measures 86 degrees and Angle C measures 41 degrees. On Quadrilateral J K L M, side K L measures 16 units and side L M measures 17 units. Angle J measures 133 degrees.
The two figures above are congruent. Find the measure of the angle that isn't labeled on either figure.
To find the measure of the angle that isn't labeled on either figure, we can use the fact that the two figures are congruent. Congruent figures have the same shape and size, so their corresponding sides and angles are equal.
Let's consider the corresponding angles in the two figures:
- Angle A in Quadrilateral ABCD corresponds to Angle J in Quadrilateral JKLM.
- Angle B in Quadrilateral ABCD corresponds to Angle K in Quadrilateral JKLM.
- Angle C in Quadrilateral ABCD corresponds to Angle L in Quadrilateral JKLM.
- Angle D in Quadrilateral ABCD corresponds to Angle M in Quadrilateral JKLM.
We are given that Angle D in Quadrilateral ABCD measures 86 degrees. Therefore, Angle M in Quadrilateral JKLM also measures 86 degrees.
Since all angles in a quadrilateral add up to 360 degrees, we can find the measure of the angle that isn't labeled by subtracting the sum of the labeled angles from 360.
The sum of the labeled angles in Quadrilateral ABCD is: Angle A + Angle B + Angle C + Angle D = 86 + 41 + 180 + 86 = 393 degrees.
Thus, the measure of the angle that isn't labeled on either figure is: 360 - 393 = -33 degrees.
Therefore, the measure of the angle that isn't labeled on either figure is -33 degrees.