Yes, two right angles can be adjacent to one another. In the letter "T", it's formed by two adjacent right angles.
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Adjacent angles will be right by each other and equal 180 degrees. Vertical angles will be opposite and equal to each other.
No vertical angles are across from each other & adjacent angles are beside but opposite from each other.
adjacent angles
Adjacent angles.
Draw to lines intersecting each other. The angles across from each other will be both congruent and adjacent