The watari-yagura-mon was constructed at adjacent angles to each side within the gate.

Also, each pair of adjacent angles forms a straight line and the two angles are supplementary.

In geometry, adjacent angles, often shortened as adj.

Angles that share a common vertex and edge but do not share any interior points are called adjacent angles.

In geometry, two angles are adjacent angles if they share a common vertex and side, but have no common interior points.

Adjacent angles are supplementary.

A side and two adjacent angles given (ASA)

In a right trapezoid (also called right-angled trapezoid), two adjacent angles are right angles.

More precisely, if a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles.

A right tangential trapezoid is a tangential trapezoid where two adjacent angles are right angles.

A convex quadrilateral is a trapezoid if and only if it has two adjacent angles that are supplementary, that is, they add up 180 degrees.

Since either of a pair of vertical angles is supplementary to either of the adjacent angles, the vertical angles are equal in measure.

For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary.

These follow from the previous proposition by applying the fact than opposite angles on intersecting lines equal (Prop. 15) and that adjacent angles on a line are supplementary (Prop. 13).

The history of the theorem can be divided into four parts: knowledge of Pythagorean triples, knowledge of the relationship among the sides of a right triangle, knowledge of the relationships among adjacent angles, and proofs of the theorem within some deductive system.

He knows that two right angles are equal to the sum of all the contiguous angles which proceed from one point in a straight line; and he goes on to produce one side of his triangle, thus forming two adjacent angles which are together equal to two right angles.