answer this question---**Question 2** 1 pts 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. m∠PQS = [blank] ° **Question 3** 2 pts Lines p and q intersect to form adjacent angles 1 and 2.

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We have perpendicular rays PQ and QR, with point S in the interior of angle PQR. We need to find the measure of angle PQS given the expressions for both angles. Since the rays are perpendicular, angle PQR equals 90 degrees. Using the Angle Addition Postulate, the sum of angles PQS and SQR equals the whole angle PQR. This gives us the equation: 4 plus 7a, plus 9 plus 4a, equals 90. Now let's solve the equation step by step. First, we combine like terms: 4 plus 9 equals 13, and 7a plus 4a equals 11a, giving us 13 plus 11a equals 90. Next, we subtract 13 from both sides to get 11a equals 77. Finally, dividing both sides by 11, we find that a equals 7. Now we substitute a equals 7 back into the expression for angle PQS. We have m angle PQS equals 4 plus 7 times a, which becomes 4 plus 7 times 7, equals 4 plus 49, equals 53 degrees. Therefore, the measure of angle PQS is 53 degrees. Let's summarize our solution. We used the fact that perpendicular rays form a 90-degree angle, applied the Angle Addition Postulate, set up the equation, solved for a equals 7, and found that m angle PQS equals 53 degrees. We can verify this is correct since 53 plus 37 equals 90 degrees.