The Earth's Hardest Geometry Problems

The problems here reflect the order of difficulty on most standardized exams. These questions test your ability to read the question correctly. Most students are not aware how tricky the wording is. We at BeatTheTest recommend that you read through all of the questions first, and then proceed with answering them. Feel free to talk to your math teachers in high school about any questions you got wrong in this book.

1)

Parallelogram GHIJ has angle J equal to 5y + √16 and angle H equal to 7y - 20. What is the sum of angles G and I equal to?

  • I) 180
  • J) 128
  • M) 116
  • N) 360
  • O) 232

2)

Point Q is the center of the circle in the adjacent diagram and US is the diameter of the circle. The perimeter of the circle is equal to 12π. What is the area of square LMNO?

  • B) 24π
  • D) 12π
  • E) 12
  • F) 144
  • G) 144π

3)

In the figure, if triangle BEF is an isosceles triangle and angle X = 63°, what is the measure of angle Y?

  • I) 75°
  • J) 83°
  • M) 45°
  • N) 72°
  • O) 90°

4)

In the adjacent diagram, what is the angle LMN equal to if angle PON is equal to 136°

  • B) 180°
  • D) 44°
  • E) 180° - y
  • F) 136°
  • G) Cannot be determined from the data provided

5)

Triangle FGH has an area of 120 and triangle JBH has an area of 176 (the heights are given). What is the value of FJ - 20 ?

  • I) 40
  • J) 60
  • M) 50
  • N) 10
  • O) Cannot be determined from the data provided

6)

WX and YZ are parallel lines. Angle A equals 75° and angle B equals 155°. What is angle C equal to?

  • I) 75°
  • J) 55°
  • M) 100°
  • N) 105°
  • O) 80°

7)

Find the length of diagonal WY in rectangle WXYZ to the nearest tenth.

  • I) 10.1
  • J) 12
  • M) 11.2
  • N) 10
  • O) Cannot be determined from the data provided.

8)

In the diagram, quadrilateral OXYZ is a rectangle. Segment LM is perpendicular to OZ. OM is equal to 36 and XM is equal to 45. What is the length of OX?

  • I) 25
  • J) 35
  • M) 27
  • N) 36
  • O) Cannot be determined from the data provided.