Geometry
⏱ ~3-min readAceMark GuideWhat this topic is really about
The circumference of a circle is calculated using the formula C = pi * d, where d is the diameter. Since the diameter is 10, the circumference is 10pi. Option A is incorrect because it mistakenly uses the radius instead of the diameter in the formula, while option D incorrectly calculates the circle's area.
Using the distance formula, the distance is the square root of (4 - 1)^2 + (6 - 2)^2, which simplifies to the square root of 9 + 16, or 5. This forms a classic 3-4-5 right triangle. Option D is incorrect because it simply adds the horizontal and vertical distances together instead of finding the diagonal.
See the mechanism
Option A is correct because the interior angles of any triangle must sum to exactly 180 degrees, and subtracting 50 and 70 from 180 leaves 60. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.
An exam-style question, fully explained
A triangle has angles 50° and 70°. The third angle is:
- Identify what the question tests: A triangle has angles 50° and 70°..
- Option A is correct because the interior angles of any triangle must sum to exactly 180 degrees, and subtracting 50 and 70 from 180 leaves 60.
- Option B is incorrect because a third angle of 70 degrees would result in a total sum of 190 degrees, violating basic geometric principles.
Traps the examiner sets
- Option B is incorrect because a third angle of 70 degrees would result in a total sum of 190 degrees, violating basic geometric principles.
- Distractors like 110 or 130 are incorrect because they result from basic multiplication errors rather than applying the correct formula.
- Option A is incorrect because it mistakenly uses the radius instead of the diameter in the formula, while option D incorrectly calculates the circle's area.
- Option D is incorrect because it simply adds the horizontal and vertical distances together instead of finding the diagonal.
- Option C is incorrect because 17 is part of the 8-15-17 triple, not the 5-12-13 triple.
Test your recall
Answer each from memory — you'll see instantly whether you're right and why.
Run a focused 10-question mini-mock on Geometry and see it stick.
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