Question

PQ=PS , <PRS= 25 degree and <PQT= 110 degree. Find the value of x​

Answer 1

Answer:

45°

Step-by-step explanation:

<PQT + <PQS = 180° [Linear Pair]

110° + <PQS = 180°

Therefore, <PQS = 180° – 110° = 70°

<RSQ = <PSQ = 70° [Angles opposite to equal sides are equal]

<PSQ + <PSR = 180° [Linear Pair]

70° + <PSR = 180°

<PSR = 180° – 70° = 110°

<PSR + < PRS + <RPS = 180° [Angle Sum Property of a Triangle]

110° + 25° + x = 180°

135° + x = 180°

x = 180° – 135° = 45°

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