Ready to put your triangle, polygon and angle smarts to the test? Dive into our free Chapter 3 Geometry Test and see if you have what it takes to ace it! This engaging quiz is designed to help you polish skills in angle relationships, properties of shapes, and problem-solving strategies, while preparing you for top scores. Explore key concepts, challenge misconceptions, and check your chapter 3 geometry test answers to track your progress. For practice, revisit fundamentals in our geometry chapter 1 test , then tackle the next level with the geometry chapter 3 test . Ready to get started? Click "Begin" and conquer Chapter 3 today!
What is the sum of the interior angles of any triangle?
180°
90°
360°
270°
In Euclidean geometry, the interior angles of a triangle always add up to 180°. You can see this by drawing a line parallel to one side and creating alternate interior angles that sum to a straight line. This fundamental fact applies to all triangles regardless of shape. For more details, visit Math Is Fun.
In an equilateral triangle, what is the measure of each interior angle?
60°
45°
90°
30°
Equilateral triangles have all three sides equal and therefore all three interior angles are equal. Since the sum of the interior angles of any triangle is 180°, each angle must be 180° ÷ 3 = 60°. This property holds for every equilateral triangle. More can be learned at Math Is Fun.
What is the sum of the interior angles of a quadrilateral?
360°
180°
540°
720°
A quadrilateral can be divided into two triangles, each with angles summing to 180°. Therefore, the total interior angle sum is 2 × 180° = 360°. This applies to any four-sided polygon in Euclidean space. See Math Is Fun for more polygon angle sums.
What is the measure of each interior angle of a regular hexagon?
120°
90°
150°
135°
A regular hexagon has six equal sides and angles. The sum of its interior angles is (6–2)×180° = 720°, and dividing by 6 gives 120° per angle. This formula applies to any regular n-gon. Learn more at Math Is Fun.
In triangle ABC, AB = AC. What type of triangle is ABC?
Isosceles
Scalene
Equilateral
Right
A triangle with exactly two equal sides is called isosceles. Here, AB and AC are equal, so the triangle has two congruent sides and two congruent base angles. This definition distinguishes it from scalene (no equal sides) and equilateral (three equal sides). More on triangle types: Math Is Fun.
An exterior angle of a triangle measures 110°. If the two opposite interior angles are 50° and 60°, is this correct?
Yes, an exterior angle equals the sum of the two opposite interior angles.
No, it equals the adjacent interior angle only.
No, it equals 180° minus the adjacent interior angle.
Yes, but only in a right triangle.
In any triangle, an exterior angle is equal to the sum of the two non-adjacent interior angles. Here those angles are 50° and 60°, summing to 110°, which matches the given exterior angle. This is a well-known triangle exterior angle theorem. Read more at Math Is Fun.
What is the sum of the exterior angles of any convex polygon, one at each vertex?
360°
180°
540°
720°
The sum of the exterior angles of any convex polygon, taking one exterior angle at each vertex, is always 360°, regardless of the number of sides. This holds because you effectively rotate a full circle as you traverse the polygon. More explanation at Math Is Fun.
In a triangle, one angle measures 90° and another measures 45°. What is the third angle?
45°
30°
60°
90°
The sum of interior angles of a triangle is 180°. Subtracting the known angles, 180° ? 90° ? 45° = 45°, so the third angle measures 45°. This shows the triangle is also isosceles right. More at Math Is Fun.
A regular polygon has each interior angle equal to 140°. How many sides does it have?
9
7
8
10
The formula for each interior angle of a regular n-gon is (n?2)×180°/n. Setting this equal to 140° gives (n?2)*180 = 140n, so 180n?360 = 140n, leading to 40n = 360 and n = 9. Details at Math Is Fun.
In a right triangle with legs of lengths 3 and 4, what is the length of the hypotenuse?
5
6
7
4
By the Pythagorean theorem, the hypotenuse c satisfies c² = 3² + 4² = 9 + 16 = 25, so c = 5. This fundamental relation holds in any right triangle. More at Math Is Fun.
What is the sum of the interior angles of a pentagon?
540°
360°
720°
600°
A pentagon has five sides, so its interior angles sum to (5?2)×180° = 3×180° = 540°. This is derived from dividing into three triangles. More on polygon angle sums at Math Is Fun.
What is the measure of each interior angle in a regular 15-gon?
156°
168°
150°
160°
For a regular n-gon, each interior angle is (n?2)×180°/n. Substituting n = 15 gives (13×180)/15 = 2340/15 = 156°. This calculation applies to any regular polygon. See Wikipedia for further details.
0
{"name":"What is the sum of the interior angles of any triangle?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"What is the sum of the interior angles of any triangle?, In an equilateral triangle, what is the measure of each interior angle?, What is the sum of the interior angles of a quadrilateral?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}
Study Outcomes
Understand Triangle Properties -
Recognize and describe key characteristics of triangles, including side length and angle measures, to build a solid foundation in triangle theory.
Classify Triangles and Polygons -
Distinguish between different types of triangles and polygons based on side counts and angle measures for accurate geometric categorization.
Apply Angle Relationships -
Utilize angle theorems and relationships, such as complementary, supplementary, and vertical angles, to solve for unknown angle measures.
Calculate Angle Sums -
Compute interior and exterior angle sums for various polygons by applying geometric formulas and theorems.
Identify Key Geometry Vocabulary -
Recall and use essential terms from Chapter 3 to improve your communication and understanding of geometric concepts.
Analyze Geometry Problems -
Evaluate and solve quiz questions with instant feedback to reinforce learning and correct misconceptions in real time.
Cheat Sheet
Angle Relationships Fundamentals -
On a geometry chapter 3 test, you'll see complementary, supplementary, vertical, and linear pairs. Complementary angles sum to 90°, while supplementary add to 180°; for example, if one angle is 30°, its complement is 60°. A quick mnemonic is "Comp = 90°, Sup = 180°" to keep them straight.
Triangle Angle Sum & Classification -
The interior angles of any triangle sum to 180°, so knowing two angles lets you find the third (e.g., 50° + 60° leaves 70°). Classify triangles by sides (scalene, isosceles, equilateral) and by angles (acute, right, obtuse) for quick recall. Remember Pythagorean triples (3-4-5) for right triangles when practicing chapter 3 geometry test answers.
Polygon Angle Sum & Regular Polygons -
Use the formula (n−2)×180° to find the sum of interior angles in an n-sided polygon; for a pentagon (n=5), it's 540°. Each exterior angle of any regular polygon measures 360°/n, so a regular hexagon has 60° exterior angles. This handy formula is a charter for accuracy on the geometry chapter 3 test.
Triangle Congruence & Similarity Criteria -
Congruence shortcuts SAS, ASA, SSS, and RHS let you prove triangles are identical in shape and size, while AA, SAS, and SSS test similarity for proportional sides. For example, showing two triangles share two angles (AA) guarantees similarity, a staple in chapter 3 test a geometry quiz. Visualizing tick marks on corresponding sides helps cement these criteria quickly.
Triangle Inequality & Exterior Angle Theorem -
The Triangle Inequality states any side must be shorter than the sum of the other two; if a question gives 2 and 5, the third side must be less than 7 but greater than 3 (|5−2|). The Exterior Angle Theorem adds that an exterior angle equals the sum of its two remote interior angles, a frequent concept in chapter 3 geometry test questions. Picture "exterior = back interior + other back" to ace answers.
