Question 25

∠ACD is an obtuse angle.

In triangle ACD, extending segment DC to point B creates the angle ∠ACD, which is greater than 90 degrees, making it the obtuse angle in this configuration.

A) ∠CAD

Angle ∠CAD is formed by the line segments CA and AD. Since it is one of the interior angles of triangle ACD, it must be acute, measuring less than 90 degrees. Therefore, it cannot be considered an obtuse angle.

B) ∠ACD

Angle ∠ACD is formed by the extended line DC and line AC. In this scenario, as segment DC is extended to point B, angle ∠ACD becomes greater than 90 degrees, thus qualifying it as an obtuse angle.

C) ∠ADC

Angle ∠ADC is another interior angle of triangle ACD. This angle is acute, as it is less than 90 degrees. Consequently, it does not fit the criteria for being an obtuse angle.

D) ∠ACB

Angle ∠ACB is formed by line segments AC and CB. While this angle may also be an interior angle in the extended figure, it remains acute as it measures less than 90 degrees. Thus, it cannot be classified as an obtuse angle.

Conclusion

The angle ∠ACD is definitively the obtuse angle in the context of the triangle and the extension of segment DC. All other angles, ∠CAD, ∠ADC, and ∠ACB, are either acute or do not exceed 90 degrees, thereby failing to meet the criteria for being classified as obtuse.