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.
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°.
