Grade: Grade 10 Subject: Mathematics Unit: Geometry Theorems Lesson: 6 of 6 SAT: Geometry+Trigonometry ACT: Math

Unit Quiz

Quiz Instructions

This quiz assesses your understanding of all geometry theorem concepts covered in this unit. Complete all 10 questions without looking at your notes first, then check your answers.

Topics Covered

  • Triangle Angle Sum Theorem
  • Exterior Angle Theorem
  • Isosceles Triangle Theorem
  • Inscribed Angle Theorem
  • Central Angle Theorem
  • Word problems and applications

Scoring Guide

  • 9-10 correct: Excellent - Ready to move on!
  • 7-8 correct: Good - Review missed concepts
  • 5-6 correct: Fair - Additional practice recommended
  • Below 5: Review the unit lessons before retaking

Quiz Questions

Question 1: In triangle ABC, angle A = 47 degrees and angle B = 68 degrees. What is angle C?

Solution: Using Triangle Angle Sum: 47 + 68 + C = 180

115 + C = 180

Answer: C = 65 degrees

Question 2: The exterior angle at vertex C of triangle ABC is 138 degrees. If angle A = 72 degrees, what is angle B?

Solution: By Exterior Angle Theorem: Exterior angle = sum of non-adjacent interior angles

138 = 72 + B

Answer: B = 66 degrees

Question 3: An isosceles triangle has a vertex angle of 44 degrees. What is the measure of each base angle?

Solution: Base angles are equal. Let each = x.

44 + x + x = 180

44 + 2x = 180

2x = 136

Answer: Each base angle = 68 degrees

Question 4: In a circle, a central angle measures 110 degrees. What is the measure of an inscribed angle that subtends the same arc?

Solution: Inscribed angle = (1/2) x Central angle

Inscribed angle = (1/2) x 110

Answer: 55 degrees

Question 5: An inscribed angle in a circle measures 28 degrees. What is the measure of the central angle subtending the same arc?

Solution: Central angle = 2 x Inscribed angle

Central angle = 2 x 28

Answer: 56 degrees

Question 6: The angles of a triangle are in the ratio 2:3:5. Find all three angles.

Solution: Let angles be 2x, 3x, and 5x.

2x + 3x + 5x = 180

10x = 180

x = 18

Answer: 36 degrees, 54 degrees, and 90 degrees

Question 7: In an isosceles triangle, one base angle is (2x + 15) degrees and the vertex angle is (3x - 10) degrees. Find the value of x and all three angles.

Solution: Both base angles are equal. Sum of angles = 180.

(2x + 15) + (2x + 15) + (3x - 10) = 180

7x + 20 = 180

7x = 160

x = 160/7 is approximately 22.86

Base angles: 2(22.86) + 15 = 60.7 degrees each

Vertex angle: 3(22.86) - 10 = 58.6 degrees

Answer: x = 160/7; base angles are approximately 60.7 degrees each; vertex angle is approximately 58.6 degrees

Question 8: An inscribed angle subtends a diameter (semicircle) of a circle. What is the measure of this inscribed angle?

Solution: A diameter corresponds to a central angle of 180 degrees.

Inscribed angle = (1/2) x 180

Answer: 90 degrees (Thales' Theorem)

Question 9: In triangle PQR, the exterior angle at R is (4x + 20) degrees. Angle P = (x + 30) degrees and angle Q = (2x + 10) degrees. Find x and the measure of the exterior angle at R.

Solution: By Exterior Angle Theorem:

4x + 20 = (x + 30) + (2x + 10)

4x + 20 = 3x + 40

x = 20

Exterior angle at R: 4(20) + 20 = 100 degrees

Answer: x = 20; exterior angle at R = 100 degrees

Question 10: Two inscribed angles in the same circle subtend the same arc. If one inscribed angle is 52 degrees, what is the other inscribed angle?

Solution: Inscribed angles subtending the same arc are congruent.

Answer: 52 degrees

Self-Assessment

After completing the quiz, count your correct answers and use the scoring guide above to evaluate your mastery.

Review Recommendations

  • Missed questions 1-2: Review Triangle Angle Sum and Exterior Angle Theorems
  • Missed questions 3, 7: Review Isosceles Triangle Theorem
  • Missed questions 4-5, 8, 10: Review Inscribed and Central Angle Theorems
  • Missed questions 6, 9: Practice algebraic setup and solving

Next Steps

  • Scored 9-10: Congratulations! You have mastered geometry theorems. Move on to the next unit.
  • Scored 7-8: Review the specific topics where you made errors, then retake the quiz.
  • Scored 5-6: Work through Guided Practice and Common Mistakes again before retaking.
  • Scored below 5: Start from Triangle Theorems and work through the entire unit again.

Additional Resources

  • Return to any lesson for review
  • Create flashcards for the key theorems
  • Practice with SAT/ACT released questions on geometry