Question

Explain two procedures that you can use to draw adjacent angles with given measures.

Answer 1

Procedure Nº 1

For example, if you you are asked to draw adjacents angles of 60º, you can construct an Obtuse Triangle (using a ruler and and a protractor to mesure the angles or you can use a compass) with angles of 30º,30º and 120º. You can bisect the angle of 120º, and you will obtain two adjacents angles of 60º.


Procedure Nº 2

If you are asked to draw adjacents angles of 30º, you can construct a triangle with angles of 60º, 60º and 60º, which is known as "Equiangular triangle"(All the three interior angles have the same value). You can use a ruler and a protactor, or the ruler and a compass to make this, because the sides of this triangle have the same lenght, so you can draw a segment, then you must open the compass with that measure and making a mark to complete the triangle. Then, you can bisect one of the angles and you will have two adjacent angles of 30º.

Answer 2

As you have not talked about polygon, but let me start from here ,if you are taking a triangle ABC the adjacent angles of A are angle B and angle C.

If we are taking Quadrilateral ABCD into consideration the adjacent angle of A are angle B and angle D.

Now coming to a point , if we have to draw adjacent angles passing through a point then that point is starting point of three rays .

Explanation:

Adjacent angles :Two angles are said to be adjacent if their non common arms lie on opposite side of common arm. In terms of rays the two rays should lie on opposite side of third ray.Suppose OA , OB and OC are three rays, taking OB as third ray OA and OC will lie on opposite side of ray OB.

1. When two angles are supplementary

First draw a line. Mark a point P on it. Mark two points S and T on opposite sides of Point P. From P draw a ray P Q.The two angles ∠QPS and ∠QPT are adjacent angles.

2. Suppose two angles are ∠AOB=60° and ∠AOC=60°. Ray OA is common.Ray OB and Ray OC will lie in opposite sides of Ray OA.

Or

Draw an angle of 120°, draw it's bisector .it's bisector will be Ray OA.

I have depicted pictures for this.

Also if ∠AOB=30° and ∠AOC=45°,taking OA as a common ray , Ray OB and ray OC will lie on opposite side of common ray OA.