1.(v) Find the remainder when is divided by
6. In Fig. 6.44, the side QR of PQR is produced to a point S. If the bisectors of PQR and PRS meet at point T, then prove that QTR = QPR.
5. In Fig. 6.43, if PQ PS, PQ SR, SQR = 28° and QRT = 65°, then find the values of x and y.
4. In Fig. 6.42, if lines PQ and RS intersect at point T, such that PRT = 40°, RPT = 95° and TSQ = 75°, find SQT.
3. In Fig. 6.41, if AB DE, BAC = 35° and CDE = 53°, find DCE.
2. In Fig. 6.40, X = 62°, XYZ = 54°. If YO and ZO are the bisectors of XYZ and XZY respectively of XYZ, find OZY and YOZ.
1. In Fig. 6.39, sides QP and RQ of PQR are produced to points S and T respectively. If SPR = 135° and PQT = 110°, find PRQ.
6. In Fig. 6.33, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB CD.
5. In Fig. 6.32, if AB CD, APQ = 50° and PRD = 127°, find x and y.
4. In Fig. 6.31, if PQ ST, PQR = 110° and RST = 130°, find QRS.
[Hint : Draw a line parallel to ST through point R.]
3. In Fig. 6.30, if AB CD, EF CD and GED = 126°, find AGE, GEF and FGE.
2. In Fig. 6.29, if AB CD, CD EF and y : z = 3 : 7, find x.
1. In Fig. 6.28, find the values of x and y and then show that AB CD.
6. It is given that XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ZYP, find XYQ and reflex QYP.
5. In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that
4. In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.
3. In Fig. 6.15, PQR = PRQ, then prove that PQS = PRT.
2. In Fig. 6.14, lines XY and MN intersect at O. If and a : b = 2 : 3, find c.
1. In Fig. 6.13, lines AB and CD intersect at O. If AOC + BOE = 70° and BOD = 40°, find BOE and reflex COE.
15.12) For the wave on a string described in Exercise 15.11, do all the points on the string oscillate with the same (a) frequency, (b) phase, (c) amplitude? Explain your answers. (ii) What is the amplitude of a point 0.375 m away from one end?