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Angles in Parallelograms Quiz

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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°.

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Solving the Equation

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

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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°.

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