**Problem Statement:**In the figure, \( m \angle ABC = 78^\circ \) and \( m \angle ABD = 32^\circ \). Find the measure of \( x \).**Diagram Explanation:**The diagram consists of three points \( A \), \( B \), and \( C \) forming angles at point \( B \). There is also a point \( D \) on the plane of the triangle such that \( \angle ABD = 32^\circ \).- Point \( A \) is upwards.- Point \( B \) is at the vertex and to the left.- Point \( C \) is on the right.- Point \( D \) is between \( A \) and \( C \).With these points:- \( \angle ABC = 78^\circ \)- \( \angle ABD = 32^\circ \)- \( \angle DBC = x^\circ \)**Question:**What is the measure of \( x \)?**Multiple Choice Answers:**- \( 58^\circ \)- \( 46^\circ \)- \( 32^\circ \)- \( 78^\circ \)**Solution:**Since angle \( \angle ABC \) is made up of angles \( \angle ABD \) and \( \angle DBC \), we have:\[\angle ABC = \angle ABD + \angle DBC\]Given, \( \angle ABC = 78^\circ \) and \( \angle ABD = 32^\circ \), so:\[78^\circ = 32^\circ + x\]Solving for \( x \):\[x = 78^\circ - 32^\circ\]\[x = 46^\circ\]Therefore, the measure of \( x \) is \( 46^\circ \).**Answer:**The correct answer is \( 46^\circ \).

Name: **Problem Statement:**In the figure, \( m \angle ABC = 78^\circ \) an
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: **Problem Statement:**In the figure, \( m \angle ABC = 78^\circ \) and \( m \angle ABD = 32^\circ \). Find the measure of \( x \).**Diagram Explanation:**The diagram consists of three points \( A \), \( B \), and \( C \) forming angles at point \( B