Question

look at this diagram: diagram shows two parallel vertical lines ( overleftrightarrow{eg} ) (with ( e ) top, ( g ) bottom) and ( overleftrightarrow{bd} ) (with ( b ) top, ( d ) bottom). a transversal line ( overleftrightarrow{ha} ) intersects ( overleftrightarrow{eg} ) at ( f ) and ( overleftrightarrow{bd} ) at ( c ), with ( h ) left, ( a ) right, and arrows indicating line directions. if ( overleftrightarrow{bd} ) and ( overleftrightarrow{eg} ) are parallel lines and ( mangle bca = 51^circ ), what is ( mangle dca )? ( square^circ )

Explanation:

Step1: Identify angle relationship

Since \( BD \) is a straight line, \( \angle BCA \) and \( \angle DCA \) are supplementary angles, meaning their sum is \( 180^\circ \).

Step2: Calculate \( m\angle DCA \)

We know \( m\angle BCA = 51^\circ \), so we use the formula \( m\angle DCA = 180^\circ - m\angle BCA \).
Substituting the value, we get \( m\angle DCA = 180^\circ - 51^\circ = 129^\circ \).

Answer:

\( 129 \)