Answer:
- (x, y, z) = (74, 37, 25)
- all acute angles are 74°
- all obtuse angles are 106°
Step-by-step explanation:
The usual rules at an intersection of lines apply:
- vertical angles are congruent
- linear pairs are supplementary
In addition, where a transversal crosses parallel lines, ...
- corresponding angles are congruent
This means, in effect, for this geometry where parallel lines cross parallel lines, all acute angles have the same measure, all obtuse angles have the same measure, and the obtuse angles are supplementary to the acute angles.
x° = 180° -106° = 74° . . . . . . x and 106 are supplementary
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2y° = x° . . . . . . . . . . . . . . x and 2y are corresponding
y = 74/2 = 37 . . . substitute for x, divide by 2
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(4z +6)° = 106° . . . . . . obtuse angles are congruent
4z = 100 . . . subtract 6
z = 100/4 = 25
The variable values are ...
All obtuse angles are 106°; all acute angles are 74°.
