LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

CONSTRUCTION OF ANGLES

__CONSTRUCTION OF ANGLES -__

**Constructing angles involves using a compass and a straightedge (ruler) to create specific angles. Here are the steps for constructing angles:**

__Constructing an Angle of a Given Measure:-__

__Materials Needed:-__

**Compass****Straightedge (Ruler)**

__Steps :-__

__Draw a Ray (Initial Side):-__Start by drawing a ray (a straight line that extends in one direction) using the straightedge. This will be one side of your angle, called the initial side.__Place the Compass at the Vertex:-__Put the pointed end of the compass on the endpoint of the initial side (vertex of the angle).__Open the Compass:-__Open the compass to a length that is more than half the expected measure of the angle. This will ensure that the arc you draw intersects the initial side.__Draw an Arc:-__Keeping the compass settings fixed, draw an arc that intersects the initial side. This arc will be the second side of the angle.__Draw the Final Side:-__Without changing the compass settings, place the compass on the intersection point of the arc and the initial side. Draw another arc that intersects the previous arc.__Draw the Angle:-__Use the straightedge to draw a line connecting the vertex to the point where the two arcs intersect. This line forms the final side of the angle.

**A) Constructing a Specific Angle (e.g., 60 degrees):-**

**Steps:-**

__Draw a Ray (Initial Side):-__Start by drawing a ray using the straightedge. This will be one side of your angle.__Place the Compass at the Vertex:-__Put the pointed end of the compass on the endpoint of the initial side.__Set the Compass to the Desired Angle:-__Open the compass to a specific angle measurement (e.g., 60 degrees).__Draw an Arc:-__Keeping the compass settings fixed, draw an arc that intersects the initial side.__Draw the Final Side:-__Without changing the compass settings, place the compass on the endpoint of the initial side. Draw another arc that intersects the previous arc.__Draw the Angle:-__Use the straightedge to draw a line connecting the vertex to the point where the two arcs intersect. This line forms the final side of the angle.

**B. Constructing a 90-Degree Angle (Right Angle):-**

**Draw a straight line using a ruler.****Place the compass at one end of the line, and draw an arc that intersects the line.****Without changing the compass width, place the compass at the intersection point on the line, and draw another arc.****The intersection of the two arcs is the right angle (90 degrees).**

**C. Constructing a 45-Degree Angle:-**

**Draw a straight line using a ruler.****Place the compass at one end of the line and draw an arc that intersects the line.****Without changing the compass width, place the compass at the other end of the line, and draw another arc.****The intersection of the line and the arc is the 90-degree angle.****Without changing the compass width, place the compass at the intersection point, and draw an arc above the line.****The angle between the original line and the new arc is 45 degrees.**

**D. Constructing a 30-Degree Angle:-**

**Draw a straight line using a ruler.****Place the compass at one end of the line and draw an arc that intersects the line.****Without changing the compass width, place the compass at the intersection point on the line, and draw another arc.****The intersection of the line and the second arc is the 60-degree angle.****Without changing the compass width, place the compass at the intersection point, and draw an arc below the line.****The angle between the original line and the****new arc is 30 degrees.**

**These constructions are basic and assume you have a ruler and compass. For more complex constructions involving specific angles or geometric shapes, additional steps and constructions may be necessary.**