# Constructing Angles

In this section you will learn constructing angles."Construction" in Geometry means to draw shapes, angles or lines accurately.

In constructing-angles, mostly we use compass and ruler.

**Construction of Angles equal to a given angle**

Draw an angle of measure 70

^{0}. Make a copy of it using ruler and compasses.

Step 1: With the help of a protractor, draw an angle ∠DAP of measure 70

^{0}.

Step 2: Draw a line l and a point P on it.

Step 3: Place the compasses at A and draw an arc to cut the rays of ∠A at B and C.

Step 4: Use the same compasses setting to draw an arc with P as center, cutting l in Q.

Step 5: Set your compasses to the length BC with the same radius.

Step 6: Place the compasses pointer at Q and draw the arc to cut the arc drawn earlier in R.

Step 7: Join PR. This gives ∠P. It has the same as ∠DAP.

∴ ∠DAP = ∠RPQ.

**Example 2 :**Draw an angle of 60

^{0}using compass and then draw a copy of angle 60.

**Steps of constructing angles :**

Step 1 :Draw a ray PC.

Step 2 : Place the pointer of the compasses at P and draw an arc of convenient radius which cuts the ray PC at a point A.

Step 3 : With the pointer at A (as centre) and with same radius now draw an arc that cuts the previous one at point B.

Step 4 : Join PB. We obtain ∠BPA whose measure is 60

^{0}.

step 5 : Now draw another ray XY

Step 6 : Place the pointer of the compasses at X and draw an arc of convenient radius which cuts the ray XY at a point M.

Step 7 : With the pointer at M (as centre) and with same radius now draw an arc that cuts the previous one at point N.

Step 8 : Join XN. We obtain ∠NXM whose measure is equal to ∠BPA = 60

^{0}.

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**Practice**

1) Given angle is 35

^{0}. Construct an angle which equal to 35

^{0}.

2) for obtaining angle 105

^{0}, which two angles you will bisect.

**Geometrical Constructions**

• Basic Geometric Constructions

• Construction of Line Segment

• Bisecting a Line Segment

• Constructing Angles

• Bisecting Angles

• Constructing Parallel Lines

• Construction of Triangle (SSS)

• SAS Triangle Construction

• ASA Triangle Construction

• HL Triangle Construction (Rhs -construction)

• Constructing Quadrilaterals

• Constructing Triangles(when sum of sides or perimeter is given)

• Basic Geometric Constructions

• Construction of Line Segment

• Bisecting a Line Segment

• Constructing Angles

• Bisecting Angles

• Constructing Parallel Lines

• Construction of Triangle (SSS)

• SAS Triangle Construction

• ASA Triangle Construction

• HL Triangle Construction (Rhs -construction)

• Constructing Quadrilaterals

• Constructing Triangles(when sum of sides or perimeter is given)