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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°?
What is the measure of the smaller angle in a parallelogram if the difference between its two angles is 40°?
If one angle in a parallelogram is known to be x and the other is x + 40°, what is the equation to find x?
If one angle in a parallelogram is known to be x and the other is x + 40°, what is the equation to find x?
How would you calculate the smaller angle of a parallelogram if the larger angle measures 80°?
How would you calculate the smaller angle of a parallelogram if the larger angle measures 80°?
What is the difference in measurement between the two angles of a parallelogram when one is 50°?
What is the difference in measurement between the two angles of a parallelogram when one is 50°?
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If the smaller angle of a parallelogram is 70°, what would be the measure of the larger angle?
If the smaller angle of a parallelogram is 70°, what would be the measure of the larger angle?
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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
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Let the two angles be x and y.
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The difference between the two angles is given as 40°, so we can write: |x - y| = 40°
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Since consecutive angles are supplementary:
- x + y = 180°
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We now have a system of two equations with two unknowns:
- |x - y| = 40°
- x + y = 180°
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We can consider two cases for the difference equation:
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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°
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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°
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Therefore, the smaller angle in the parallelogram is 70°.
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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.
