Question

identify all obtuse angles in the drawing below.
options:
∠bmc, ∠cme
∠bmd, ∠amc, ∠ame
∠ame
∠amb, ∠cmd, ∠dme

Explanation:

Step1: Define obtuse angles

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

Step2: Analyze each angle

• $\angle BMC$: Right angle ($90^\circ$, not obtuse)
• $\angle CME$: Obtuse (greater than $90^\circ$, less than $180^\circ$)
• $\angle BMD$: Acute (less than $90^\circ$, not obtuse)
• $\angle AMC$: Obtuse (greater than $90^\circ$, less than $180^\circ$)
• $\angle AME$: Obtuse (greater than $90^\circ$, less than $180^\circ$)
• $\angle AMB$: Straight angle ($180^\circ$, not obtuse)
• $\angle CMD$: Acute (less than $90^\circ$, not obtuse)
• $\angle DME$: Acute (less than $90^\circ$, not obtuse)

Step3: Match with options

The set of obtuse angles is $\angle BMD, \angle AMC, \angle AME$.

Answer:

$\angle BMD, \angle AMC, \angle AME$