Question

Angle 75 diagram and angle 15,150

Answer 1

Answer:

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Step-by-step explanation:

Refer the attachment below

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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)