# In Fig. 6.42, 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

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