Question

Transversal d intersects lines e and f to form 8 angles. The angles formed with line e, clockwise from top left, are 35 degrees, blank, 6, blank. The angles formed with line f, clockwise from top left are 5, 57 degrees, blank, 4.
For the diagram shown, find the measures of angles 4, 5, and 6.

m∠4 =
degrees
m∠5 =
degrees
m∠6 =
degrees

Answer 1

To solve for the measures of angles 4, 5, and 6, we will utilize the properties of angles formed by a transversal intersecting two parallel lines.

1. **Finding angle \( m∠5 \)**:
- Angle \( m∠5 \) is adjacent to angle \( m∠6 \) on line e. Angles on a straight line sum up to \( 180^\circ \).
- Thus, if angle \( m∠6 = 6^\circ \):
\[
m∠5 + 6 = 180
\]
\[
m∠5 = 180 - 6 = 174^\circ
\]

2. **Finding angle \( m∠4 \)**:
- Angle \( m∠4 \) is vertically opposite to angle \( m∠5 \).
- Hence,
\[
m∠4 = m∠5 = 174^\circ
\]

3. **Finding angle \( m∠6 \)**:
- From the first step, we already have the value of \( m∠6 \) given as \( 6^\circ \).

Thus, the measures of the angles are:

- \( m∠4 = 174 \) degrees
- \( m∠5 = 174 \) degrees
- \( m∠6 = 6 \) degrees

So,

\[
m∠4 = 174^\circ,
m∠5 = 174^\circ,
m∠6 = 6^\circ
\]