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Complete 3. a and 3. b

Complete 3. a and 3. b-example-1
User Amom
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Answer:

  • x = 5
  • a = f = 14°
  • b = c = d = e = 166°

Explanation:

Given alternate interior angles at parallel lines have measures x +9 and 4x -6, you want to know the value of x and the measures of all of the angles.

Alternate interior angles

Where a transversal crosses parallel lines, alternate interior angles are congruent:

4x -6 = x +9

3x = 15 . . . . . . . . add 6-x

x = 5

The value of x is 5.

Other angles

In the figure shown, all of the acute angles are congruent, and all of the obtuse angles are congruent.

a = x +9 = 5 +9

a = 14 . . . . . degrees

f = a = 14°

The obtuse angles are supplementary to the acute angles:

b = c = d = e = 180° -a = 166°

User Sep Roland
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