Angles in Parallelograms Quiz

Choose a study mode

Play Quiz

Study Flashcards

Spaced Repetition

Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the measure of the smaller angle in a parallelogram if the difference between its two angles is 40°?

80° (correct)
50°
70°
60°

If one angle in a parallelogram is known to be x and the other is x + 40°, what is the equation to find x?

x + (x - 40°) = 180°
x + (x + 40°) = 360°
x + (x + 40°) = 180° (correct)
x - (x + 40°) = 180°

How would you calculate the smaller angle of a parallelogram if the larger angle measures 80°?

It is impossible to find
Subtract 40° from 180° (correct)
Subtract 40° from 80°
Add 40° to 80°

What is the difference in measurement between the two angles of a parallelogram when one is 50°?

<p>40° (B)</p> Signup and view all the answers

If the smaller angle of a parallelogram is 70°, what would be the measure of the larger angle?

<p>110° (D)</p> Signup and view all the answers

Flashcards

Parallelogram Angle Problem

The difference between the two angles of a parallelogram is 40°. This problem asks us to find the smaller angle of the parallelogram.

Consecutive Angles in a Parallelogram

In a parallelogram, the sum of the two adjacent angles (consecutive angles) is always 180°.

Angle Representation

Let the smaller angle of the parallelogram be x. The larger angle is then x + 40°.

Equation Setup

Since the angles are consecutive, the sum of the smaller and larger angle is 180°. Therefore, x + (x + 40°) = 180°.

Signup and view all the flashcards

Solving the Equation

Solving the equation for x, we get x = 70°. Therefore, the smaller angle of the parallelogram is 70°.

Signup and view all the flashcards

Study Notes

A parallelogram has four sides, with opposite sides parallel and equal in length.
Opposite angles in a parallelogram are equal.
Consecutive angles in a parallelogram are supplementary (their sum is 180°).

Finding the Smaller Angle

Let the two angles be x and y.
The difference between the two angles is given as 40°, so we can write: |x - y| = 40°
Since consecutive angles are supplementary:
- x + y = 180°
We now have a system of two equations with two unknowns:
- |x - y| = 40°
- x + y = 180°
We can consider two cases for the difference equation:
Case 1: x - y = 40° - Substituting x = y + 40° into the second equation: - (y + 40°) + y = 180° - 2y + 40° = 180° - 2y = 140° - y = 70° - x = 110°
Case 2: y - x = 40° - Substituting y = x + 40° into the second equation: - x + (x + 40°) = 180° - 2x + 40° = 180° - 2x = 140° - x = 70° - y = 110°
Therefore, the smaller angle in the parallelogram is 70°.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your understanding of the properties of angles in parallelograms with this quiz. Explore the relationships between opposite and consecutive angles while applying given conditions. Solve equations to find the measures of the angles in different cases.