Question

Lines a and b are parallel and lines e and f are parallel.

Vertical and parallel lines a and b are intersected by horizontal lines e and f. At the intersection of lines a and e, the top left angle is angle 1 and the top right angle is angle 2. At the intersection of lines b and e, the bottom left angle is angle 3. At the intersection of lines b and f, the uppercase right angle is angle 4 and the bottom left angle is angle 5.

If m1 = 89°, what is m5?

1
89
91
179

Answer 1

To find the value of \( m_5 \), we can use the properties of parallel lines and the angles formed by transversals.

Given that lines \( a \) and \( b \) are parallel, and lines \( e \) and \( f \) are also parallel, we can apply the corresponding angles postulate and the consecutive interior angles theorem.

1. **Identify the angles:**
- At the intersection of line \( a \) and line \( e \):
- \( m_1 = 89^\circ \) (top left angle)
- \( m_2 \) (top right angle) will be equal to \( m_1 \) because they are corresponding angles.
- Therefore, \( m_2 = 89^\circ \).

2. **At the intersection of lines \( b \) and \( e \):**
- \( m_3 \) (the bottom left angle) is corresponding to \( m_1 \) because lines \( a \) and \( b \) are parallel, and lines \( e \) and \( f \) are also parallel.
- So, \( m_3 = 89^\circ \).

3. **At the intersection of lines \( b \) and \( f \):**
- The angle \( m_4 \) (uppercase right angle) is vertically opposite to \( m_2 \). Hence, \( m_4 \) is also \( 89^\circ \).
- \( m_5 \) (the bottom left angle at the intersection of line \( b \) and line \( f \)) will be supplementary to \( m_4 \) because they form a straight line (this means they add up to \( 180^\circ \)).
- Thus, \( m_4 + m_5 = 180^\circ \), leading to \( 89^\circ + m_5 = 180^\circ \).

4. **Solve for \( m_5 \):**
\[
m_5 = 180^\circ - 89^\circ = 91^\circ
\]

Thus, the measure of angle \( m_5 \) is \( \boxed{91} \).