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Quizzes > High School Quizzes > Mathematics

Practice Quiz 7-1: Angles & Parallelograms

Conquer Unit 7: Practice Parallelograms & Shape Answers

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Paper art promoting a trivia quiz on Polygon and Parallelogram Angles for high school students.

What is the sum of the interior angles of a triangle?
270 degrees
90 degrees
360 degrees
180 degrees
The sum of the interior angles in any triangle is 180 degrees, which is a fundamental theorem in Euclidean geometry. This property holds for all triangles.
What is the formula for the sum of the interior angles of a polygon with n sides?
(n - 2) × 180 degrees
n × 180 degrees
(n - 1) × 180 degrees
(n + 2) × 180 degrees
The formula (n - 2) × 180 calculates the sum by dividing the polygon into (n - 2) triangles, each contributing 180 degrees. This formula applies universally to any polygon.
In a parallelogram, what is the relationship between opposite angles?
They are equal
They are all different
They are supplementary
They are complementary
Opposite angles in a parallelogram are congruent, meaning they have equal measures. This is one of the defining properties of a parallelogram.
For any convex polygon, if the polygon is regular, how do you calculate each exterior angle?
Multiply 360 by the number of sides
Divide 180 by the number of sides
Subtract the interior angle from 180
Divide 360 by the number of sides
The sum of the exterior angles of any convex polygon is always 360 degrees. When the polygon is regular, each exterior angle is equal to 360 divided by the number of sides.
Which characteristic best describes a rectangle, a special type of parallelogram?
Consecutive angles are equal
All angles are 90 degrees
Opposite angles are equal
All angles are obtuse
A rectangle has all of its interior angles equal to 90 degrees, which makes it unique among parallelograms. This property defines a rectangle and distinguishes it from other types of parallelograms.
What is the measure of each interior angle of a regular pentagon?
120 degrees
90 degrees
108 degrees
100 degrees
A regular pentagon's interior angles sum to (5 - 2) × 180 = 540 degrees. Dividing 540 by 5 leads to each interior angle measuring 108 degrees.
What is the sum of the interior angles of a hexagon?
540 degrees
680 degrees
600 degrees
720 degrees
A hexagon has 6 sides, so the sum of its interior angles is calculated as (6 - 2) × 180 = 720 degrees. This formula is independent of whether the polygon is regular or irregular.
In a parallelogram, if one angle measures 70 degrees, what is the measure of its adjacent angle?
70 degrees
120 degrees
110 degrees
90 degrees
Adjacent angles in a parallelogram are supplementary, meaning they add up to 180 degrees. Thus, if one angle is 70 degrees, the adjacent angle must be 180 - 70 = 110 degrees.
What is the measure of the exterior angle of a regular octagon?
90 degrees
40 degrees
60 degrees
45 degrees
For a regular octagon, the sum of the exterior angles is always 360 degrees. Dividing 360 by 8 gives an exterior angle of 45 degrees.
How many diagonals does a decagon (10-sided polygon) have?
30
35
25
20
The formula for the number of diagonals in a polygon is n(n - 3)/2. For a decagon, this is 10(10 - 3)/2 = 35 diagonals.
If each exterior angle of a regular polygon measures 24 degrees, how many sides does the polygon have?
24
15
12
18
Since the sum of the exterior angles of any convex polygon is 360 degrees, dividing 360 by 24 gives 15 sides. This is a standard method to determine the number of sides in a regular polygon.
In a parallelogram, what is the relationship between consecutive (adjacent) angles?
They are always 90 degrees
They are supplementary (sum to 180 degrees)
They are complementary
They are equal
In any parallelogram, consecutive angles are supplementary, meaning they always add up to 180 degrees. This is a defining property that helps distinguish parallelograms from other quadrilaterals.
In a regular polygon, how is the interior angle related to the exterior angle at each vertex?
Interior angle = 180° - exterior angle
Interior angle = exterior angle - 180°
Interior angle = 360° - exterior angle
Interior angle = interior angle × exterior angle
The interior and exterior angles at a vertex of any polygon are supplementary, which means they add up to 180 degrees. Therefore, the interior angle can be found by subtracting the exterior angle from 180 degrees.
If the measure of each interior angle of a regular polygon is 150 degrees, how many sides does the polygon have?
6
10
12
8
Subtracting the interior angle from 180° gives an exterior angle of 30°. Dividing 360° by 30° results in 12 sides. This is a standard method to determine the number of sides of a polygon.
In a parallelogram, if one angle measures 95 degrees, what is the measure of the angle opposite to it?
105 degrees
95 degrees
85 degrees
120 degrees
Opposite angles in a parallelogram are equal. Thus, if one angle is 95 degrees, the angle directly opposite to it is also 95 degrees.
A regular polygon has a prime number of sides and an integer measure for each exterior angle. Which of the following could be the measure of its exterior angle?
60 degrees
90 degrees
108 degrees
72 degrees
A regular polygon's exterior angle is found by dividing 360 degrees by the number of sides. With a prime number of sides, possible values include 360/3 = 120° and 360/5 = 72°. Among the options provided, 72 degrees is the only valid integer measure.
A quadrilateral with one pair of opposite angles equal and consecutive angles supplementary is known as a:
Isosceles Trapezoid
Kite
Cyclic Quadrilateral
Parallelogram
The properties described - opposite angles being equal and consecutive angles being supplementary - are the defining characteristics of a parallelogram. These features set parallelograms apart from other types of quadrilaterals.
In a regular polygon, if each interior angle measures 156 degrees, how many sides does the polygon have?
18
12
24
15
Subtracting the interior angle from 180° gives an exterior angle of 24°. Dividing the full angle sum of 360° by 24° yields 15 sides, which is the number of sides for the polygon.
A parallelogram has one angle represented by x, where 2x + 30 = 180. What is the measure of the angle adjacent to x?
105 degrees
120 degrees
75 degrees
90 degrees
Solving the equation 2x + 30 = 180 gives x = 75 degrees. Since consecutive angles in a parallelogram are supplementary, the adjacent angle must be 180 - 75 = 105 degrees.
For any convex polygon with n sides, if one interior angle is increased by 10% without changing the polygon's convexity, what is the new sum of the interior angles?
(n-2)×180 degrees plus 10%
360 degrees
(n-2)×180 degrees multiplied by 1.1
(n-2)×180 degrees
The sum of the interior angles of a convex polygon depends solely on the number of sides and is given by (n-2)×180 degrees. Changing one angle does not alter this invariant sum as long as the figure remains a polygon.
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Study Outcomes

  1. Calculate the interior and exterior angle measures of various polygons.
  2. Apply the properties of parallelograms to determine unknown angle values.
  3. Analyze geometric diagrams to identify relationships between adjacent and vertical angles.
  4. Evaluate angle sum properties in polygons and parallelograms to solve targeted problems.

Quiz 7: Polygons & Parallelograms Answers Cheat Sheet

  1. Sum of interior angles - Every polygon has a secret code to its interior angles: (n−2)×180°, where n is the number of sides. Crack it and you'll find a pentagon has 540° of angles to play with! Think of it as slicing a polygon into triangles. Interior Angles Explained
    2. mathsisfun.com
  2. Regular polygon interior angle - When all sides and angles are happy twins, you can find each interior angle by dividing the total sum by n: [(n−2)×180°]/n. For a hexagon, that dish gives you a cool 120° per angle. It's like cutting an angle pie into equal slices! Regular Polygons Guide
    3. mathsisfun.com
  3. Sum of exterior angles - No matter how many sides you count, the exterior angles of any polygon will always swirl up to 360°. Extend each side at its vertex and add them up - you'll circle a full rotation. This trusty rule helps you avoid angle chaos in weird shapes. Exterior Angles Overview
    4. mathbitsnotebook.com
  4. Regular polygon exterior angle - In a perfectly balanced polygon, each exterior angle is just 360° divided by n. For an octagon, you get 45° per angle - cozy and uniform! It's a fast formula for quick geometry wins. Exterior Angle Tips
    5. mathsisfun.com
  5. Interior and exterior are supplementary - At any vertex, the interior and its adjacent exterior angle join forces to make 180°. This dynamic duo helps you solve for missing angles with ease. It's like two puzzle pieces that perfectly complement each other! Supplementary Angles Deep Dive
    6. gmatfree.com
  6. Parallelogram side & angle rules - A parallelogram flaunts opposite sides that are both parallel and equal in length, with its opposite angles matching each other. Plus, each pair of adjacent angles sum to 180° - like buddies leaning on one another. Recognizing these patterns speeds up your quadrilateral quests! Parallelogram Properties
    7. mathsisfun.com
  7. Parallelogram diagonals bisect each other - The diagonals of a parallelogram are your proof buddies: they cut each other exactly in half. This nifty property is a favorite for congruence and similarity challenges. With diagonals on your side, tackling proofs gets a serious upgrade! Diagonal Bisector Secrets
    8. mathsisfun.com
  8. Rhombus special diagonals - A rhombus is just a parallelogram that loves equality - every side is the same length. Its diagonals are perpendicular bisectors, creating perfect right angles at their intersection. It's a geometry artist's dream for symmetry! Rhombus Rundown
    9. mathsisfun.com
  9. Rectangle diagonal traits - In a rectangle, you've got four right angles that give the diagonals special powers - they're equal in length and they bisect each other. These features make solving for unknown angles and lengths a breeze. It's like having a built‑in measurement tool! Rectangle Rundown
    10. mathsisfun.com
  10. Square's stylish diagonals - A square takes the best of rectangles and rhombi: equal angles and equal sides. Its diagonals are the ultimate multitaskers - they're equal, bisect at right angles, and carve the square into four congruent right triangles. Squaring up your studies has never been this sleek! Square Spotlight
    11. mathsisfun.com
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