Question

In the figure shown below, PQRS is a parallelogram. QU=TU , ∠PUT=110° and ∠RQT=50°

Answer 1

what we find now for this question

Answer 2

Please write the complete question dear mate

Here , ∠ RTQ = ∠ PUQ = 90° , As given : QT ⊥ SR and QU ⊥ PS

Now from angle sum property of triangle we get in ∆ RTQ :

∠ RTQ + ∠ R + ∠ RQT = 180° , Substitute values from given diagram we get :

90° + ∠ R + 50° = 180°

∠ R = 40°

We know adjacent angles are supplementary in parallelogram , So

∠ R + ∠ S = 180° , Substitute value

of " ∠ R " as we calculated above and get :

40° + ∠ S = 180° ,

∠ S = 140°

We know opposite angles in parallelogram are equal to each other , So

∠ P = ∠ R and ∠ Q = ∠ S , So

∠ P = 40° and ∠ Q = 140°

Now from angle sum property of triangle we get in ∆ PUQ :

∠ PUQ + ∠ P + ∠ PQU = 180° , Substitute values from given diagram and as we calculated above we get :

90° + 40° + ∠ PQU = 180°

∠ PQU = 50° --1

And

∠ Q = ∠ PQU + ∠ TQU + ∠ RQT From given diagram and now we substitute values and get :

140° = 50° + ∠ TQU + 50° ,

∠ TQU = 40°

Therefore,

∠ R = 40° , ∠ TQU = 40° , ∠ P = 40° and ∠ S = 140°