Question

in the adjoining figure,AB||CD,angle BPR=60° and angle CQP=110°.find all the angles of ∆pqr and angles apq​

Answer 1

Answer

First, we will find the value of the ∠APQ.

As we know that, the lines AB and CD are parallel to each other. We can conclude that the line PQ is a transversal line. We know that the interior angles on same side of transversal always adds up to 180°. So,

Measurement of ∠APQ :

$\sf \dashrightarrow {110}^{\circ} + \angle{APQ} = {180}^{\circ}$

$\sf \dashrightarrow \angle{APQ} = {180}^{\circ} - {110}^{\circ}$

$\sf \dashrightarrow \angle{APQ} = {70}^{\circ}$

Now, we will find the values of all the angles in the triangle given.

As we know that all the angles forming a straight line always equals up to 180°. So,

Measurement of ∠QPR :

$\sf \dashrightarrow {60}^{\circ} + {70}^{\circ} + \angle{QPR} = {180}^{\circ}$

$\sf \dashrightarrow {130}^{\circ} + \angle{QPR} = {180}^{\circ}$

$\sf \dashrightarrow \angle{QPR} = {180}^{\circ} - {130}^{\circ}$

$\sf \dashrightarrow \angle{QPR} = {50}^{\circ}$

We know that all the angles forming a straight line always equals up to 180°. So,

Measurement of ∠PQR :

$\sf \dashrightarrow {110}^{\circ} + \angle{PQR} = {180}^{\circ}$

$\sf \dashrightarrow \angle{PQR} = {180}^{\circ} - {110}^{\circ}$

$\sf \dashrightarrow \angle{PQR} = {70}^{\circ}$

We know that all the angles in a triangle always adds up to 180°. So,

Measurement of ∠PRQ :

$\sf \dashrightarrow {50}^{\circ} + {70}^{\circ} + \angle{PRQ} = {180}^{\circ}$

$\sf \dashrightarrow {120}^{\circ} + \angle{PRQ} = {180}^{\circ}$

$\sf \dashrightarrow \angle{PRQ} = {180}^{\circ} - {120}^{\circ}$

$\sf \dashrightarrow \angle{PRQ} = {60}^{\circ}$