Yes, two angles can be both supplementary and congruent
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Angles that are congruent and supplementary must be right angles.
No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.
congruent
Yes, intersecting chords in a circle create a pair of vertical angles, which are always congruent. However, these angles are not supplementary; supplementary angles are those that sum to 180 degrees. Vertical angles formed by intersecting chords are equal to each other, meaning they are not supplementary unless they each measure 90 degrees, which would make them right angles.
They are supplementary
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Angles that are congruent and supplementary must be right angles.
They are congruent angles
Vertical angles are always, by definition, congruent. Note: If the two vertical angles are right angles then they are both congruent and supplementary.
No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.
congruent
Yes, intersecting chords in a circle create a pair of vertical angles, which are always congruent. However, these angles are not supplementary; supplementary angles are those that sum to 180 degrees. Vertical angles formed by intersecting chords are equal to each other, meaning they are not supplementary unless they each measure 90 degrees, which would make them right angles.
All supplementary angles do not form a linear pair. The opposite angles of any quadrilateral inscribed in a circle (a cyclic quadrilateral) are supplementary but they are not a linear pair. However, all linear pair are supplementary.
They can be but not always because supplementary angles add up to 180 degrees.
Give us a break! -- A 3° angle is congruent to another 3° angle, but their sum is only 6° , not 180°. -- Congruent angles are always equal, but supplementary angles don't have to be equal.
Supplementary Congruency Theorem