If the sum of two angles is greater than 180°, then which of the following is not possible for the two angles?
One obtuse angle and one acute angle
One reflex angle and one acute angle
Two obtuse angles
Two right angles
Goal: Sum must be greater than 180°.
Option A: One obtuse + one acute
Obtuse: \(90^\circ < \text{angle} < 180^\circ\)
Acute: \(0^\circ < \text{angle} < 90^\circ\)
Example: \(120^\circ + 70^\circ = 190^\circ\)
\(190^\circ > 180^\circ\). Possible.
Option B: One reflex + one acute
Reflex: \(\text{angle} > 180^\circ\)
Acute: \(\text{angle} < 90^\circ\)
Sum: \(> 180^\circ + 0^\circ = > 180^\circ\)
Always greater than 180°. Possible.
Option C: Two obtuse angles
Each obtuse: \(> 90^\circ\)
Smallest sum: \(91^\circ + 91^\circ = 182^\circ\)
\(182^\circ > 180^\circ\). Possible.
Option D: Two right angles
Right angle: \(90^\circ\)
Sum: \(90^\circ + 90^\circ = 180^\circ\)
Not greater than 180°. Not possible.
Answer: Option D