To calculate the shaded angles in quadrilaterals, we can use the property that the sum of all interior angles in a quadrilateral is 360 degrees.
For Quadrilateral (a):
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Let's denote the angles:
- Angles A, B, C, and D in the quadrilateral.
- We know one angle \( A = 57° \) and we need to find the shaded angle.
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The formula for the sum of angles in a quadrilateral is: \[ A + B + C + D = 360° \]
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Assuming the shaded angle is angle B, we can set up the equation like this: \[ 57° + B + C + D = 360° \]
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If we have the values of angles C and D, we could plug them in and solve for B. But without additional information, we cannot solve for B.
For Quadrilateral (b):
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Similar to quadrilateral (a), we denote the angles:
- Angles A, B, C, and D.
- We know one angle \( A = 63° \) and we need to find the shaded angle (let's say angle B).
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Using the same formula, we have: \[ 63° + B + C + D = 360° \]
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Again, without values for angles C and D, we cannot determine B explicitly.
Conclusion:
In order to calculate the shaded angles accurately, we need more information about the other angles in each quadrilateral. If you can provide the additional angles or any relationships between the angles in the diagrams, I can help you solve for the shaded angles.
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