Question

(hint: add angle numbers to the figure)
find all unknown angle measures.

1. find ( mangle a ), ( mangle b ) and ( mangle c )

diagram: a horizontal line intersected by two lines (one with a ( 112^circ ) angle, the other forming angles ( a ), ( b ), ( c ) with the horizontal line)
( mangle a = _ quad mangle b = _ quad mangle c = ___ )

Explanation:

Step1: Find \( m\angle b \)

\( \angle b \) and the \( 112^\circ \) angle are corresponding angles (since the lines are parallel, as indicated by the congruent angle marks), so \( m\angle b = 112^\circ \).

Step2: Find \( m\angle a \) and \( m\angle c \)

\( \angle a \) (or \( \angle c \)) and \( \angle b \) are supplementary (they form a linear pair), so \( m\angle a + m\angle b = 180^\circ \) and \( m\angle c + m\angle b = 180^\circ \).
For \( m\angle a \):
\( m\angle a = 180^\circ - 112^\circ = 68^\circ \)
For \( m\angle c \):
\( m\angle c = 180^\circ - 112^\circ = 68^\circ \) (also, \( \angle a \) and \( \angle c \) are vertical angles, so they are equal)

Answer:

\( m\angle a = 68^\circ \), \( m\angle b = 112^\circ \), \( m\angle c = 68^\circ \)