Question

in the figure, m∠abd = 156°. the figure shows a point b with three rays: ba going up and left, bc going right, and bd going down and right. the angle between bc and bd is 32°, and the angle between ba and bc is marked with a ?.

Explanation:

Step1: Identify angle relationship

We know that \( m\angle ABD = m\angle ABC + m\angle CBD \). Let \( m\angle ABC = x \) (the unknown angle), \( m\angle ABD = 156^\circ \), and \( m\angle CBD = 32^\circ \).

Step2: Solve for unknown angle

Using the angle addition postulate, we can write the equation \( 156^\circ = x + 32^\circ \). To find \( x \), we subtract \( 32^\circ \) from both sides: \( x = 156^\circ - 32^\circ \).
Calculating the right - hand side: \( 156 - 32 = 124 \), so \( x = 124^\circ \).

Answer:

The measure of the unknown angle ( \( m\angle ABC \)) is \( 124^\circ \)