An illustration shows two parallel slanting lines m and l intersecting a vertical line k. The angles formed at the intersection of lines l and k are 1, 2, 4, and 3. The angles 1 and 4 are opposite to each other while angles 2 and 3 are opposite to each other. The angles formed at the intersection of lines m and k are 5, 6, 8, and 7. The angles 5 and 8 are opposite to each other while angles 6 and 7 are opposite to each other.

Question

An illustration shows two parallel slanting lines m and l intersecting a vertical line k. The angles formed at the intersection of lines l and k are 1, 2, 4, and 3. The angles 1 and 4 are opposite to each other while angles 2 and 3 are opposite to each other. The angles formed at the intersection of lines m and k are 5, 6, 8, and 7. The angles 5 and 8 are opposite to each other while angles 6 and 7 are opposite to each other.
What is  m∠1
  if  m∠4=25°
 ?

GPT-4o mini · Answer

In the given problem, we have two parallel lines \( m \) and \( l \) intersecting a vertical line \( k \). The angles formed at the intersections can be analyzed based on the properties of vertical angles and angles formed by parallel lines.

Since angles 1 and 4 are opposite to each other at the intersection of line l and k, they are vertical angles. This means that:

\[ m∠1 = m∠4 \]

Given that \( m∠4 = 25° \), we can substitute this value into the equation:

\[ m∠1 = 25° \]

Thus, the measure of angle 1 is:

\[ \boxed{25°} \]