In the given figure, if line PQ and RS intersect at point 'T' such that ∠PRT= 40° , ∠RPT= 95° and ∠TSQ = 75°, find ∠SQT.

Open in App

Solution

Step 1: Find the ∠PTR.

Given : ∠PRT = 40°, ∠RPT = 95° and ∠TSQ = 75°.

Angle sum property of triangle is, the sum of all three angles is equal to 180°

∠PRT + ∠RPT + ∠PTR = 180 (Angle sum property of triangle)

∠PTR = 180° - (40° + 95°)

∠PTR = 45°

Then, ∠STQ = ∠PTR = 45° (vertically opposite angle)

Step 2: Find the ∠SQT .

Apply angle sum property again in ΔSQT.

Dictate and write:

∠STQ + ∠TSQ + ∠SQT = 180°

∠SQT = 180° - (45° + 75°)

∠SQT = 60°

Hence ∠SQT is 60°

Suggest Corrections

Similar questions

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

P Q

R S

T

∠ P R T = 40^{\circ}, ∠ R P T = 95^{\circ}

∠ T S Q = 75^{\circ}

∠ S Q T

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

P Q

R S

T

∠ P R T = 40^{\circ}, ∠ R P T = 95^{\circ} a n d ∠ T S Q = 75^{\circ}, f i n d ∠ S Q T

∠ P R T = 40^{\circ}

∠ R P T = 95^{\circ}

∠ T S Q = 75^{\circ}

∠ S Q T

Join BYJU'S Learning Program