Answer:
(b) x=80, y=38, z=63
Explanation:
You want to know the values of x, y, and z, given they are angle measures in a diagram showing two triangles.
Linear pair
The angles that form a linear pair are supplementary:
x° +100° = 180°
x = 80 . . . . . . . . . divide by °, subtract 100
Angle sum theorem
The angle sum theorem tells you that the sum of angles in a triangle is 180°.
y° +62° +80° = 180°
y = 38 . . . . . . . . . . . . divide by °, subtract 142
In the other triangle, the same relation holds:
z° +100° +17° = 180°
z = 63 . . . . . . . . . . . . divide by °, subtract 117
The values of x, y, and z are ...
(x, y, z) = (80, 38, 63)