Question

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

Explanation:

Step1: Define obtuse angles

An obtuse angle is $90^\circ < \theta < 180^\circ$.

Step2: Analyze each angle

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

Answer:

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