Answer:
Explanation:
You want to know the values of x, y, and z, which are three angles in a figure showing two triangles that share a side and a base.
Angle sum theorem
The angle sum theorem tells you the sum of angles in a triangle is 180°. This means ...
x° +32° +46° = 180°
x = 180 -78 . . . . . . divide by °, subtract 78 from both sides
x = 102
Linear Pair
Adjacent angles that form a straight line are called a "linear pair." Their sum is 180°
y° +x° = 180°
y = 180 -x = 180 -102
y = 78
Remote interior angles
You may have noticed that the value of y is equal to the sum of the two given angles in the triangle containing x. That is, the exterior angle is equal to the sum of the remote interior angles. This is also true for the left-side triangle:
x° = z° +36°
z = x -36 . . . . . divide by °, subtract 36
z = 102 -36
z = 66
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Additional comment
The theorems cited here can be used in a number of different combinations to find the measures of these angles. We could start by finding y = 32+46 = 78, then z = 180 -36 -78 = 66, and x = 36 +66 = 102.