Which of these angles can be constructed using ruler and a pair of compasses only?

Analyze the question: We need to find which angle can be constructed with only a ruler and a pair of compasses.

Concept: With a ruler and compasses, the basic angles we can construct are:

• 90° (by constructing a perpendicular)
• 60° (by constructing an equilateral triangle)
• Angles got by bisecting these, e.g. 45°, 30°, 15°, 22.5°
• Angles got by adding or subtracting these, e.g. 120°, 75°, 105°, 135°, 150°

So an angle is constructible here if it can be built from 60° and 90° by adding, subtracting, or bisecting.

Solution: Check each option.

• 115°: It is not a multiple of 15°, so it can't be built from 60°/90° and their bisections. Not constructible this way.
• 125°: Also not a multiple of 15°. Not constructible this way.
• 135°: 135° = 90° + 45°, and 45° is the bisector of 90°. So construct 90°, then bisect another 90° to get 45°, and add them. Alternatively, 135° = 180° − 45°. This is constructible.
• 145°: Not a multiple of 15°. Not constructible this way.

Answer: Option C (135°).

Tip: In "which angle can be constructed" questions, look for multiples of 15° (15°, 30°, 45°, 60°, 75°, 90°, 105°, 120°, 135°, ...). Angles ending in 5° that aren't multiples of 15° (like 115°, 125°, 145°) are the usual distractors.