Question

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Answer 1

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Answer 2

Sum of linear pair angles = 180°

∠ABC + 130° = 180

∠ABC = 180 - 130

∠ABC = 50°

Sum of linear paired angles = 180°

∠PRQ + 140° = 180°

∠PRQ = 180° - 140°

∠PRQ = 40°

Given in question, ΔABC ≅ ΔPQR . So, ∠ABC = ∠PQR and ∠ACB = ∠PRQ

∠ABC = 50° = ∠PQR

∠PRQ = 40° = ∠ACB  

∴  In ΔTQC, ∠TQC = ∠PQR { from figure }

                    ∠TQC = 50°

                    ∠TCQ = ∠ACB { from figure }

                    ∠TCQ = 40°

Sum of all angles in a triangle = 180°

∠TCQ + ∠TQC + QTC = 180°

50° + 40° + ∠QTC = 180°

∠QTC = 180° - 90°

∠QTC = 90°

We know that opposite angles are equal,so ∠QTC = ∠ATP

∠ATP = ∠QTC = 90°

Therefore,, measure of ∠ATP is 90°

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