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This includes the answers to the 10 questions of the figure posted.


Question 1. Find w.

Answer: w = 25°

Explanation:

  • Since it is given that the segments AB and CD are parallel, you can use the fact that by the alternate interior angles postulate w is equal to 25°.

Question 2. Find x.

Answer: x = 25°

Explanation:

  • Since the measure x° forms a linear pair with the measure 25° they are supplementary angles and you can write: x + 25° = 180°.
  • Solve for x: x = 180° -25° = 155°.

Question 3. Find y

Answer: y =  155°

Explanation:

  • y and x result of the intersection of a transversal line with two parallel lines and they are corresponding angles, so they are equal: y = x = 155°.

Question 4. Find z.

Answer: z = 155°

Explanation:

  • Since the measure z° and the measure x° belong to vertical angles (they are opposite by the vertex) they are equal, and so z° = x° = 155°.

Question 5. Find x

Answer: x = 140°.

Explanation:

  • the measure x and the measure 40° are supplementary, hence x + 40° = 180°.
  • Solving for x: x = 180° - 40° = 40°.

Question 6. Find y

Answer: y = 40°

Explanation:

  • The measure y and the measure 40° are alternate interior angles, so they are equal: y = 40°.

Question 7. Find z

Answer: z = 40°

Explanation:

  • z and y are vertical angles (angles opposed  by the vertex) so they are congruent: z = y = 40°.

Question 8. Find x

Answer: x = 70°

Explanation:

  • The measure x and 70° belong to corresponding angles, since they result of the intersection of a transverse line with two parallel lines.

Question 9. Find y.

Answer: y = 70°

Explanation:

  • y and x form vertical angles (angles opposed by the vertex), so they are congruent.
  • y = x = 70°.

Question 10. Find z

Answer: z = 110°

Explanation:

  • z and x are linear pair angles, so they are suplementary: z + x = 180°
  • solve for z: z = 180° - x
  • substitue x = 70°: z = 180° - 70° = 110°.

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