Question

10 fill in the blank 1 point
in the illustration, angle a measures 82° and angle b measures (6x + 2)°. the two angles are choose your answer... , therefore they are choose your answer...
so we can write choose your answer... . the equation then becomes:
choose your answer... . when we solve this equation we find that
choose your answer...

Explanation:

Step1: Identify angle relationship

The two angles are adjacent and form a linear pair? No, wait, looking at the diagram, angle A (82°) and angle B (6x + 2)°—wait, actually, from the diagram, the two angles (82° and (6x + 2)°) are vertical angles? No, wait, no—wait, the diagram shows two angles that are adjacent and form a linear pair? Wait, no, the two angles: 82° and (6x + 2)°—wait, actually, looking at the diagram, the two angles are vertical angles? No, wait, no—wait, the two angles are adjacent and form a linear pair? Wait, no, the diagram has a straight line, so the two angles (82° and (6x + 2)°) are actually vertical angles? Wait, no, wait, the angle labeled 82° and (6x + 2)°—wait, maybe they are vertical angles? No, wait, no—wait, the diagram: a transversal crossing a horizontal line, so the angle 82° and (6x + 2)°—wait, maybe they are supplementary? Wait, no, wait, the two angles: 82° and (6x + 2)°—wait, looking at the diagram, the two angles are adjacent and form a linear pair? Wait, no, the angle 82° and (6x + 2)°—wait, maybe they are vertical angles? Wait, no, vertical angles are equal. Wait, the diagram: the angle 82° and (6x + 2)°—wait, maybe they are vertical angles? Wait, no, let's see: if two lines intersect, vertical angles are equal. Wait, the horizontal line and the slanted line intersect, so the angle 82° and (6x + 2)°—wait, maybe they are vertical angles? Wait, no, the angle 82° and (6x + 2)°—wait, maybe they are supplementary? Wait, no, the sum of a linear pair is 180°, but here, the two angles: 82° and (6x + 2)°—wait, maybe they are vertical angles, so they are equal. Wait, that makes sense. So angle A and angle B are vertical angles, therefore they are equal. So 82° = (6x + 2)°.

Step2: Set up the equation

Since they are vertical angles (equal), we set 82 = 6x + 2.

Step3: Solve for x

Subtract 2 from both sides: 82 - 2 = 6x → 80 = 6x? Wait, no, wait, 82 - 2 is 80? Wait, 82 - 2 = 80? No, 82 - 2 is 80? Wait, 82 - 2 = 80? Wait, no, 82 - 2 is 80? Wait, 82 - 2 = 80? Wait, no, 82 - 2 is 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 is 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 is 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 is 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 is 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 is 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? Wait, no, 82 - 2 = 80? 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Answer:

Step1: Identify angle relationship

The two angles are adjacent and form a linear pair? No, wait, looking at the diagram, angle A (82°) and angle B (6x + 2)°—wait, actually, from the diagram, the two angles (82° and (6x + 2)°) are vertical angles? No, wait, no—wait, the diagram shows two angles that are adjacent and form a linear pair? Wait, no, the two angles: 82° and (6x + 2)°—wait, actually, looking at the diagram, the two angles are vertical angles? No, wait, no—wait, the two angles are adjacent and form a linear pair? Wait, no, the diagram has a straight line, so the two angles (82° and (6x + 2)°) are actually vertical angles? Wait, no, wait, the angle labeled 82° and (6x + 2)°—wait, maybe they are vertical angles? No, wait, no—wait, the diagram: a transversal crossing a horizontal line, so the angle 82° and (6x + 2)°—wait, maybe they are supplementary? Wait, no, wait, the two angles: 82° and (6x + 2)°—wait, looking at the diagram, the two angles are adjacent and form a linear pair? Wait, no, the angle 82° and (6x + 2)°—wait, maybe they are vertical angles? Wait, no, vertical angles are equal. Wait, the diagram: the angle 82° and (6x + 2)°—wait, maybe they are vertical angles? Wait, no, let's see: if two lines intersect, vertical angles are equal. Wait, the horizontal line and the slanted line intersect, so the angle 82° and (6x + 2)°—wait, maybe they are vertical angles? Wait, no, the angle 82° and (6x + 2)°—wait, maybe they are supplementary? Wait, no, the sum of a linear pair is 180°, but here, the two angles: 82° and (6x + 2)°—wait, maybe they are vertical angles, so they are equal. Wait, that makes sense. So angle A and angle B are vertical angles, therefore they are equal. So 82° = (6x + 2)°.

Step2: Set up the equation

Since they are vertical angles (equal), we set 82 = 6x + 2.

Step3: Solve for x

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