Question

For problems 1- 3 use the following situation. ZPQS with R in the interior.

O.

mZPQS = 4x, m SQR = 2x, mZRQP = 22. Find m2 SQR and mZPOS.
Option 1: m2 SQR = 8, mZPOS = 22
Option 2: m2 SQR = 4, mZPOS = 22
Option 3: m2 SQR = 8, mZPOS = 4
Option 4: m2 SQR = 4, mZPOS = 4

Answer 1

The correct values of m∠ SQR and m∠ ZPOS are 158° and 22° respectively, which do not match any of the provided options.

Step-by-step explanation:

To solve for m∠ SQR and m∠ ZPQS, we have to use the angle measures given. According to the problem, m∠ ZPQS = 4x and m∠ SQR = 2x. Given that m∠ ZRQP = 22°, and recognizing that angles ZRQP and SQR are supplementary (they add up to 180° since they form a straight line), we can set up the equation 2x + 22 = 180 to solve for x. Dividing both sides by 2, we have x + 11 = 90. Subtracting 11 from both sides, x = 90 - 11 = 79. Therefore, m∠ SQR = 2(79) = 158° and m∠ ZPQS = 4(79), but since we do not need to calculate m∠ ZPQS further to answer the problem, we can leave it as 4(79).

To find m∠ ZPOS, we consider the fact that m∠ ZRQP = 22°, and no further calculation is required as it is already given.

Therefore, m∠ SQR = 158° and m∠ ZPOS = 22°. None of the options provided in the question correctly reflects these values.