Question

identify all obtuse angles in the drawing below.

Explanation:

Step1: Recall the definition of an obtuse angle

An obtuse angle is an angle whose measure is greater than \(90^{\circ}\) and less than \(180^{\circ}\).

Step2: Analyze each option

• Option 1: \(\angle MON = 90^{\circ}\) (right - angle), \(\angle NOP\) is acute (less than \(90^{\circ}\)), \(\angle POR\) is acute (less than \(90^{\circ}\)), \(\angle ROM\) is reflex (greater than \(180^{\circ}\)).
• Option 2: \(\angle NOQ\) is acute (less than \(90^{\circ}\)).
• Option 3: \(\angle MOQ\) and \(\angle QON\) are obtuse. Let's assume the measures: If we consider the coordinate - like axes ( \(OM\perp ON\)). \(\angle MOQ\) and \(\angle QON\) are greater than \(90^{\circ}\) and less than \(180^{\circ}\).
• Option 4: \(\angle POQ\) and \(\angle QOR\) are acute (less than \(90^{\circ}\)).

Answer:

\(\angle MOQ,\angle QON\)