Question

lines m and n are parallel.
find the measure of \\(\angle a\\).
\\(m\angle a = \quad^{\circ}\\)

Explanation:

Identify the angle relationship

The lines \(M\) and \(N\) are parallel.
The angles \(47^\circ\) and \(a\) are consecutive interior angles.

Apply the consecutive interior angles theorem

Consecutive interior angles are supplementary.

$$ 47^\circ + a = 180^\circ $$

Solve for the unknown angle

Subtract \(47^\circ\) from both sides.

$$ a = 180^\circ - 47^\circ $$

$$ a = 133^\circ $$

Answer:

Lines M and N are parallel. Find the measure of \(\angle a\).

\(m\angle a =\) <blank>\(133\)</blank>\(^\circ\)