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URSE Two angles in a vertical pair have measures that add to \( 70^{\circ} \). What is the measure of each angle? (1 point) SSON CDBACK

Ask by Li Li. in the United States
Feb 02,2025

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Answer

Each angle measures 35 degrees.

Solution

Vertical angles are always congruent, meaning they have equal measures. If the two angles in a vertical pair add up to \( 70^{\circ} \), each angle must be: \[ \frac{70^{\circ}}{2} = 35^{\circ} \] **Each angle measures 35 degrees.**

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Bonus Knowledge

When dealing with vertical angles, we know that each pair of angles are equal. However, the angles in this case are supplementary, meaning they add up to 180 degrees. Given that they add to \( 70^{\circ} \), we can deduce that they’re actually part of a different relationship. Let's call the angles \( A \) and \( B \). You can express this as \( A + B = 70^{\circ} \) and since they are supplementary to another pair, you'd find that if one angle measures \( x \), then the other measures \( 70 - x \). Since these angles do not form a conventional vertical pair in our usual sense (they aren't equal), any angle that satisfies the relationship can be valid! For example, if one angle is \( 30^{\circ} \), the other will be \( 40^{\circ} \), ultimately ensuring they meet that \( 70^{\circ} \) total. Now for a fun tip: Always visualize the angles when solving problems like these! Drawing a diagram can help you see how the angles relate to one another and clarify their relationships, making problem-solving way more intuitive!

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