Question

QUESTION:
IN THE IMAGE. EXPLANATION NEEDED!


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Answer 1

Answer: The measure of angle $\angle STQ$ is $80^{\circ}$.

Step-by-step explanation: To find the measure of angle $\angle STQ$, we need to draw a parallel line segment to both $PQ \, \text{and}\, RS$, that passes from T, say $AT$.

Further, say $\angle ATQ=\, a,\, \angle ATS=\,b$

Now, in figure, we can expand the line segments $TQ \, \text{and}\,TS$  further.

Say, $\angle PQN=\, c,\, \angle RSM=\, d$.

Since, $PQ \parallel AT$

therefore, $c =\,a$ (corresponding angles)  

Similarly, $AT \parallel RS$

therefore, $b=\,d$ (corresponding angles)    

Also, since sum of linear pair of angles made on a straight line is $180^{\circ}$, therefore,  $c+ {125}^{\circ} = {180}^{\circ} \qquad \text{and} \, \, d+ {155}^{\circ} = {180}^{\circ}$

which gives $c= {55}^{\circ} \, \text {and} \,\, d= {25}^{\circ}$.

From above, $c= a= \, {55}^\circ \,\text{and}\,\, d=b= \, {25}^{\circ}$

Finally, $\angle STQ=\, a+b=\, {80}^{\circ}$.

TIP: The problrm can also be solved by using consecutive interior angles property.