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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
Assuming you are following the convention to label the vertices of the two congruent figures in the same corresponding angles, you have 3 of the 4 angles given, add up those 3
All 4 angles must add up to 360°.
So how much is missing to form the 4th angle?
thnx
To find the measure of the angle that isn't labeled on either figure, we can use the concept of congruent figures.
Since the two figures, Quadrilateral ABCD and Quadrilateral JKL, are congruent, it implies that the corresponding angles in both figures are equal.
Let's label the missing angle as angle X.
In Quadrilateral ABCD, we know that angle D measures 86 degrees and angle C measures 41 degrees. Since the sum of the interior angles of a quadrilateral is equal to 360 degrees, we can find angle B as follows:
Angle B = 360 degrees - angle D - angle C
= 360 degrees - 86 degrees - 41 degrees
= 233 degrees
Now, let's look at Quadrilateral JKL. We know that angle J measures 133 degrees. Since angle J corresponds to angle B in Quadrilateral ABCD, we can conclude that angle X (which is the missing angle) would also measure 133 degrees.
Therefore, the measure of the angle that isn't labeled on either figure is 133 degrees.
To find the measure of the angle that isn't labeled on either figure, we can use the fact that corresponding angles in congruent figures are equal.
First, let's label the unknown angle on both figures. Let's call it angle X.
In Quadrilateral ABCD, angle D is already labeled as 86 degrees, and angle C is labeled as 41 degrees. We need to find angle X.
In Quadrilateral JKLM, angle J is labeled as 133 degrees. Again, we need to find angle X.
Since the two figures are congruent, the corresponding angles are equal. So, angle X in Quadrilateral ABCD is equal to angle X in Quadrilateral JKLM.
To find angle X, we can use the fact that the sum of angles in a quadrilateral is 360 degrees.
In Quadrilateral ABCD, sum of angles = angle A + angle B + angle C + angle D = 360 degrees.
We know that angle A and angle B are not labeled, but we can find their measures using the fact that the sum of angles in a triangle is 180 degrees.
In triangle ABD, angle A + angle B + angle D = 180 degrees.
We have angle D as 86 degrees, so angle A + angle B = 180 degrees - angle D.
Now, we can substitute the values in the sum of angles equation for Quadrilateral ABCD:
angle A + angle B + angle C + angle D = 360 degrees
(angle A + angle B) + angle C + angle D = 360 degrees
[180 degrees - angle D] + angle C + angle D = 360 degrees
180 degrees + angle C = 360 degrees
angle C = 360 degrees - 180 degrees
angle C = 180 degrees
So, angle C in Quadrilateral ABCD is 180 degrees.
Now, we can find angle X using the sum of angles equation for Quadrilateral JKLM:
angle J + angle K + angle L + angle M = 360 degrees
angle X + angle K + angle L + angle M = 360 degrees
133 degrees + angle K + angle L + angle M = 360 degrees
angle K + angle L + angle M = 360 degrees - 133 degrees
angle K + angle L + angle M = 227 degrees
Since angle L is labeled as 16 degrees, we have:
angle K + 16 degrees + angle M = 227 degrees
angle K + angle M = 227 degrees - 16 degrees
angle K + angle M = 211 degrees
Now, we know that angle X in Quadrilateral ABCD is equal to angle X in Quadrilateral JKLM. So, we can equate them:
180 degrees = angle K + angle M
angle K + angle M = 180 degrees
Therefore, the measure of the angle that isn't labeled on either figure, angle X, is 180 degrees.