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First, look closely: The image displays two horizontal lines, labeled BD and EG, which appear to be parallel. A transversal line, AH, intersects both. At the intersection point F on line EG, two angles are given: one is 32° and the other is 148°. At the intersection point C on line BD, an angle labeled 'x' is shown. The goal is to find the value of 'x'. I can see that the 32° angle and the 148° angle at point F are adjacent and form a straight line, confirming they are supplementary (32 + 148 = 180). This suggests the lines are indeed parallel, as the consecutive interior angles on the same side of the transversal sum to 180°. The angle 'x' at point C appears to be a corresponding angle to the 148° angle at point F.
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Next, find information: I need to confirm the geometric relationship between the angles. Since the lines are parallel, I will use the property of corresponding angles. Angle 'x' and the 148° angle are on the same side of the transversal and in corresponding positions relative to the parallel lines. Therefore, they should be equal. I do not need to use a tool for this; the solution is derived from standard geometry principles.
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Then, review the findings: The reasoning is sound. Given that lines BD and EG are parallel (confirmed by the supplementary consecutive interior angles), the corresponding angles formed by the transversal AH must be congruent. Angle 'x' corresponds to the 148° angle.
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Final Answer:
- x = 148°
Parent Tip: Review the logic above to help your child master the concept of consecutive angles worksheet.
