Question

In the given figure , if OP//RS,angle OPQ=110 and angle QRS=130, then determine angle PQR​

Answer 1

Hey,

I have written the answer in the picture above.
I have also mentioned the derivatives.

Hope it helps. You can clarify any further doubts.

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Answer 2

Answer:

Required value of angle PQR is 60°.

Step-by-step explanation:

Here given,OP||RS.

and angle OPQ=110° and angle QRS =130°

Here in the picture,angle OPN is Straight angle.

We know Value of Straight angle is always 180°.

Here angle OPN $= {180}^{o}$

Now,angle OPN =angle OPQ+angle QPN.

Let value of angle QPN.

${180}^{o} = x + {110}^{o}$

We are separating variable and constant part,

$x = {180}^{o} - {110}^{o} \\ x = {70}^{o}$

Again here angle PNR and QRS are corresponding angles.

We know Corresponding angles are always equal.

So, angle PNR = angle QRS $= {130}^{o}$

Again angle PNR and angle PNQ are Straight angle.

So,angle PNR+angle PNQ=180°

Therefore angle PNQ=180°-130°=50°

Angle QPN,angle PNQ and angle PQN are angles of a triangle PQN.

We know sum of all angles of a triangle is 180°.

So,

angle QPN+angle PNQ + angle PQN = ${180}^{o}$

70°+50°+angle PQN=180°

angle PQN=180°-70°-50°= 60°

Now from picture it is clear that angle PQN = angle PQR

So required value of angle PQR is 60°.