**Construction Of An Angle Using Compass And Ruler**

**To draw an angle equal to a given angle**

**Given:** An angle CAB.

**To construct:** An angle RPQ equal to ∠CAB.

**Step 1:**Taking A as the centre and any convenient radius, draw an arc cutting the arms of ∠CAB at points D and E.

**Step 2:**Draw a ray PQ, with P as the centre and the same radius as above, draw an arc cutting the ray PQ at S.

**Step 3:**Taking S as the centre and radius equal to DE, draw an arc intersecting a previous arc at a point T.

**Step 4:**Join PT and produce it to form a ray PR.

**Step 5:**∠RPQ is the required angle equal to ∠CAB.**Step 6:**Verify it by measuring the angles using protractor.

**Read More:**

- Construction of an Equilateral Triangle
- Construction Of Similar Triangle As Per Given Scale Factor
- Construction Of A Line Segment
- Construction Of The Bisector Of A Given Angle
- Construction Of Perpendicular Bisector Of A Line Segment

**Construction Of Some Standard Angles**

In this section, we will learn how to construct angles of 60º, 30º, 90º, 45º and 120º with the help of ruler and compasses only.

**Construction of an Angle of 60º**

**Step 1:**Draw any ray AB.

**Step 2:**Taking A as the centre and with any suitable radius, draw an arc PQ that cuts AB at Q.

**Step 3:**Taking Q as the centre and radius equal to AQ, draw an arc cutting the previous arc PQ at R.

**Step 4:**Join AR and produce it to get AC.

**Step 5:**∠BAC is the required angle equal to 60º.

**Construction of an Angle of 30º**

**Step 1:**Draw an angle of 60° as explained before.

**Step 2:**Taking P as the centre and a radius greater than half of PQ, draw an arc. Taking Q as the centre and with the same radius draw another arc, cutting the previous arc at D.

**Step 3:**Join A and D to get the ray AD.

**Step 4:**AD is the angular bisector of ∠CAB. Therefore ∠CAD = ∠DAB = 30°, is the required angle.

**Construction of an Angle of 120°**

**Step 1:**Draw a ray BC.

**Step 2:**Taking B as the centre arid with any suitable radius, draw an arc PQ cutting BC at Q.

**Step 3:**Taking Q as the centre and BQ as a radius, draw an arc cutting arc PQ at R. Taking R as the centre and with the same radius, cut an arc PQ at another point S.

**Step 4:**Join BS and produce it to get BA.

**Step 5:**∠ABC is the required angle of measure of 120°.

**Construction of an Angle of 90º**

**Step 1:**Draw a line AC and mark a point B on it.

**Step 2:**Taking B as the centre and with any suitable radius, draw an arc PQ cutting AC at P and Q.

**Step 3:**Taking P and Q as the centres and with any convenient radius, draw arcs intersecting each other at D.

**Step 4:**Join B and D to get the ray BD.

Then, ∠ABD = ∠DBC = 90° is the required angle.

**Construction of an Angle of 45º**

**Step 1:** Draw an angle of 90° as explained before.

**Step 2:** Taking Q as a centre and a radius more than half of QR, draw an arc.

**Step 3:** Taking R as the centre and the same radius, draw an arc cutting the previous arc at E.

**Step 4:** Join A and E to get the ray AE.

**Step 5:** AE is the angular bisector of ∠DAC. Therefore, ∠DAE = ∠EAC = 45° is the required angle. Verify it by using a protractor.

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