![In Fig. 6.31, if PQ ST, PQR = 110° and RST = 130°, find QRS. [Hint : Draw a line parallel to ST through point R.] Q.4](https://ask.truemaths.com/wp-content/uploads/2021/08/If-PQ-ST-Q.4.png)
Please give me the best way for solving the problem of class 9th ncert math of Lines and Angles chapter of math of class 9th of exercise 6.2of question no 4 what is the tricky way for solving this question In Fig. 6.31, if PQ ST, PQR = 110° and RST = 130°, find QRS. [Hint : Draw a line parallel to ST through point R.]
First, construct a line XY parallel to PQ.
We know that the angles on the same side of transversal is equal to 180°.
So, PQR+QRX = 180°
Or,QRX = 180°-110°
∴ QRX = 70°
Similarly,
RST +SRY = 180°
Or, SRY = 180°- 130°
∴ SRY = 50°
Now, for the linear pairs on the line XY-
QRX+QRS+SRY = 180°
Putting their respective values, we get,
QRS = 180° – 70° – 50°
Hence, QRS = 60°