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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.

If m∠6=140°
, what is m∠7
?

(1 point)
Responses

180°
180 degrees

140°
140 degrees

50°
50 degrees

40°

Answer 1

To solve for \( m\angle 7 \), we can use the property of angles formed by two intersecting lines.

Given that \( m\angle 6 = 140^\circ \), we need to find its adjacent angle \( m\angle 7 \). Since angles 6 and 7 are adjacent, we can use the fact that adjacent angles on a straight line sum up to \( 180^\circ \).

\[ m\angle 6 + m\angle 7 = 180^\circ \]

Substituting the value of \( m\angle 6 \):

\[ 140^\circ + m\angle 7 = 180^\circ \]

Now, we can solve for \( m\angle 7 \):

\[ m\angle 7 = 180^\circ - 140^\circ = 40^\circ \]

Thus, the answer is:

40°