Question

please say the answer with explanations ​

Answer 1

In triangle PQR,

TS is a perpendicular line bisecting PQ at S.

Therefore angle TSQ = 90° [Right Angle]

Answer 2

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According to Universal laws of triangles, The sum of all angles in a triangle is 180°. So we can say that, The sum of all angles of ∆PQR is 180°.

Hence,

• ➤ ∠PQR + ∠QRP + ∠QPR = 180°

• ➤ ∠PQR + 80° + 40° = 180°

• ➤ ∠PQR + 120° = 180°

• ➤ ∠PQR = 180° - 120°

• ➤ ∠PQR = 60° •••(1)

As ST is parallel to QR. And Side PR is reacting like a transversal. So we can say that, ∠STR and ∠QRT lie on same side of transversal so, ∠STR and ∠QRT are Linear pair.

Hence,

• ➤ ∠STR + ∠QRT = 180°

• ➤ ∠STR + 80° = 180°

• ➤ ∠STR = 180° - 80°

• ➤ ∠STR = 100° •••(2)

According to Universal rules of Quadrilaterals, The sum of all angles of Quadrilaterals is 360°. So we can say that, The sum of all angles of Quadrilateral STRQ is 360°.

Hence,

• ➤ ∠STR + ∠TRQ + ∠RQS + ∠QST = 360°

By Equation (1) and (2),

• ➤ 100° + ∠TRQ + 60° + ∠QST = 360°

As given,

• ➤ 160° + 80° + ∠TSQ = 360°

• ➤ 240° + ∠TSQ = 360°

• ➤ ∠TSQ = 360° - 240°

• ➤ ∠TSQ = 120°

Therefore,

• The measurement of ∠TSQ is 120°.

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• The measurement of ∠TSQ is 120°.