Question

which angles are obtuse? check all that apply: ∠mlk ∠dbc ∠dba ∠gfe

Explanation:

Step1: Recall obtuse angle definition

An obtuse angle is greater than $90^\circ$ and less than $180^\circ$.

Step2: Analyze each angle

• $\angle MLK$: It's a right angle ($90^\circ$), not obtuse.
• $\angle DBC$: $\angle ABC$ is a straight angle ($180^\circ$), $\angle DBA$ is acute (less than $90^\circ$), so $\angle DBC = 180^\circ - \angle DBA$, which is greater than $90^\circ$ and less than $180^\circ$ (obtuse).
• $\angle DBA$: Acute (less than $90^\circ$), not obtuse.
• $\angle GFE$: Acute (less than $90^\circ$), not obtuse.

Answer:

$\angle DBC$