Question

question
answer attempt 1 out of 5
the quadrilateral shown is a
the m∠b=

Explanation:

Step1: Identify the quadrilateral type

The quadrilateral has \( AB \parallel CD \) (indicated by the arrows) and \( BC \parallel AD \)? Wait, no, looking at the diagram, \( BC \) and \( AD \) have arrows? Wait, no, the arrows are on \( BC \) and \( AD \)? Wait, no, the diagram shows \( AB \) and \( CD \)? Wait, no, the sides \( BC \) and \( AD \) have arrows? Wait, no, the given diagram: \( B \) to \( C \) has an arrow, \( A \) to \( D \) has an arrow. Wait, actually, in a trapezoid, if two sides are parallel (the bases), then consecutive angles between the bases are supplementary. Wait, the quadrilateral is a trapezoid with \( AD \parallel BC \) (since the arrows are on \( AD \) and \( BC \), indicating they are parallel). So \( \angle A \) and \( \angle B \) are consecutive angles between the parallel sides \( AD \) and \( BC \), so they are supplementary (their measures add up to \( 180^\circ \)).

Step2: Calculate \( m\angle B \)

We know that \( m\angle A = 78^\circ \), and since \( AD \parallel BC \), \( \angle A + \angle B = 180^\circ \) (consecutive interior angles are supplementary). So we can solve for \( m\angle B \):

\( m\angle B = 180^\circ - m\angle A \)

Substitute \( m\angle A = 78^\circ \):

\( m\angle B = 180^\circ - 78^\circ = 102^\circ \)

Answer:

The quadrilateral shown is a trapezoid (specifically, a trapezoid with \( AD \parallel BC \)). The \( m\angle B = 102^\circ \).