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
140°
140 degrees
180°
180 degrees
50°
50 degrees
40°
1 answer
To find \( m∠7 \), we can use the property that angles on a straight line sum up to \( 180° \).
Since \( ∠6 \) and \( ∠7 \) are adjacent angles, we know:
\[ m∠6 + m∠7 = 180° \]
Given that \( m∠6 = 140° \), we can substitute this value into the equation:
\[ 140° + m∠7 = 180° \]
Now, we can solve for \( m∠7 \):
\[ m∠7 = 180° - 140° = 40° \]
Thus, the measure of angle \( ∠7 \) is:
\[ \boxed{40°} \]
