Question

In the given Figure if line segments PQ and RS intersect at point T, such that angle PRT= 40°, angle RPT = 95° and angle TSQ= 75° Find angle SQT=? ​

Answer 1

Step-by-step explanation:

In Triangke PRT

P + R + T = 180°

95° + 40° + T = 180°

T = 180° - 135°

T = 45°

Angle PTR = Angle STQ ( VERTICALLY OPPOSITE ANGLES)

ANGLE STQ = 45°

IN Triangle STQ

S + T + Q = 180°

75° + 45° + Q = 180°

Q = 180° - 120°

Q = 60 °

Therefore Angle SQT = 60 °.

Answer 2

Given :

<RPT = 95°

<TSQ = 75°

<PRT = 40°

To find :

We have to find <SQT.

Solution :

In ∆PRT,

<PRT + <RTP + <TPR = 180° (Angle sum property)

40° + <RTP + 95° = 180°

<RTP = 180° - 135°

==> <RTP = 45°

<RTP = <STQ (Vertically opposite angles)

==> <STQ = 45°

In ∆SQT,

<SQT + <QTS + <TSQ = 180° (Angle sum property)

<SQT + 45° + 75° = 180°

<SQT = 180° - 120°

==> <SQT = 60°

Therefore, <SQT = 60°.

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