Q21 of 50 Page 6

In Fig., if lines PQ and RS intersect at point T, such that ∠ PRT = 40°, ∠ RPT = 95°and ∠ TSQ = 75°, find ∠ SQT.

Given:


∠PRT = 40o


∠RPT = 95o and,


∠TSQ = 75o


Now according to the question,


∠PRT + ∠RPT + ∠PTR = 180o(Sum of interior angles of the triangle)


40o + 95o + ∠PTR = 180o


40o + 95o + ∠PTR = 180o


135o + ∠PTR = 180o


∠PTR = 45o


∠PTR = ∠STQ = 45o(Vertically opposite angles)


Now,


∠TSQ + ∠PTR + ∠SQT = 180o (Sum of the interior angles of the triangle)


75o + 45o + ∠SQT = 180o


120o + ∠SQT = 180o


∠SQT = 60o


More from this chapter

All 50 →
19

In Fig., if PQ || ST, ∠ PQR = 110° and∠ RST = 130°, find ∠ QRS.

 20

In Fig., 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.

 22

In Fig., ray AB and CD intersect at O.


(i) Determine y when x = 60°


(ii) Determine x when y = 40o

 23

In Fig., sides QP and RQ of Δ PQR are produced to points S and T respectively. If ∠ SPR = 135° and ∠ PQT = 110°, find ∠ PRQ.