Construction of 150 Degree Angle with the help of Compass

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150 Degree Angle

Before you understand this concept, you are advice to read: What is angle sum property ? To construct 150 degree angle we first construct 60 degree angle and its steps are as follows - 1). Use Ruler - Draw a Line segment QR of any convenient length. (as shown below) 2). Now use compass and open it to any convenient radius. And with Q as center draw an arc which cuts line segment QR at y . (as shown below) 3). Again use compass and opened to the same radius (as of step 2). And With y as center , draw an arc which cuts previous arc at X . (as shown below) 4). Join QX and extent it to P . (as shown below) 5). Above formed angle PQR = 60 Degree 6). Extend RQ to S (as shown below) 7). Now Angle PQS = 120 degree (as per Angle Sum Property); as shown below: Now, to construct at 150 degree angle, we will construct the angle bisector of above angle PQR. And its done in the following steps: 8). Now use compass and open it to any convenient radius. And with Q as center , draw an arc which cuts QR at B and PQ at A . (as shown below) 9). Again use compass and open it to same radius (as of step 8). And with A & B as center, draw two arcs which cut each other at point C (as shown below) 10). Join QC and extend to T (as shown below) 11). QT is the bisector of Angle PQR Therefore, Angle PQT = Angle TQR = half of Angle PQR Angle PQR = 60 degree (see step 5) So half of angle PQR = 60/2 = 30 degree Therefore, Angle PQT = Angle TQR = 30 degree 12). Now observe that: Angle PQS = 120° (as per step 7) Angle PQT = 30° (as per step 11) Add both the angles and we get Angle PQS + Angle PQT = 120° + 30° ..... (Statement 1) Now observe the above diagram: Angle PQS + Angle PQT = Angle SQT ..... (Statement 2) From Statement 1 and 2, we get: Angle SQT = 150° (as highlighted with pink color)