Question

which angle is a right angle? ∠abg ∠dbg ∠cbg ∠abc

Explanation:

Step1: Recall right angle definition

A right angle is \( 90^\circ \), marked by a right - angle symbol (\(\boldsymbol{\square}\)) in diagrams.

Step2: Analyze each angle

• For \(\angle ABG\): Points \(A\), \(B\), \(G\) are colinear (lie on a straight line), so \(\angle ABG = 180^\circ\) (a straight angle), not a right angle.
• For \(\angle DBG\): In the diagram, at point \(B\), the line \(BD\) is perpendicular to line \(BG\) (as indicated by the right - angle symbol at \(B\) between \(BD\) and \(BG\)'s line). So \(\angle DBG = 90^\circ\), which is a right angle.
• For \(\angle CBG\): The position of point \(C\) shows that \(\angle CBG\) is not a right angle (it is an acute or obtuse angle, not \(90^\circ\)).
• For \(\angle ABC\): The position of point \(C\) shows that \(\angle ABC\) is not a right angle (it is an acute or obtuse angle, not \(90^\circ\)).

Answer:

\(\boldsymbol{\angle DBG}\) (corresponding to the option with \(\angle DBG\) as the angle)