Please solve the following.

Question

06-02-2022
Mathematics

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Please solve the following.

Sagot :

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sqdancefan sqdancefan · Answer 1 · 2022-02-07T16:57:00-05:00

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

__

2y° = x° . . . . . . . . . . . . . . x and 2y are corresponding

y = 74/2 = 37 . . . substitute for x, divide by 2

__

(4z +6)° = 106° . . . . . . obtuse angles are congruent

4z = 100 . . . subtract 6

z = 100/4 = 25

The variable values are ...

x = 74
y = 37
z = 25

All obtuse angles are 106°; all acute angles are 74°.

Sagot :

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