Angle Relationships: Rays PQ and QR are perpendicular.

[RedTracer]

Does anyone know how to do (or even start) the following question?

Rays PQ and QR are perpendicular. Point S lies in the interior of <PQR. If m<PQS = 4+7a and m<SQR = 9+4a, find m<PQS and m<SQR.

This sign (<) means angle, not less than.

Thx

 

[pka]

If two rays are perpendicular then the angle they determine is 90.

 

[Mrspi]

Does anyone know how to do (or even start) the following question?

Rays PQ and QR are perpendicular. Point S lies in the interior of <PQR. If m<PQS = 4+7a and m<SQR = 9+4a, find m<PQS and m<SQR.

This sign (<) means angle, not less than.

Thx

If rays PQ and QR are perpendicular, what kind of angle is <PQR? It's a right angle, by the definition of perpendicular. And what is its measure? Since the measure of any right angle is 90, m<PQR = 90.

If S is in the interior of <PQR, what do you know about m<PQS + m<SQR? By the Angle Addition Postulate (or whatever name your particular text may call this),
m<PQS + m<SQR = m<PQR

Now, you've got expressions or numbers for each of these angle measures. Substitute those expressions and/or numbers for each angle measure. Solve the resulting equation for "a". Then, substitute the value of "a" into the expressions given for m<PQS and m<SQR to get the required answer.

I hope this helps you.