The shape PQRS is a parallelogram
- The measure of angle QRS is 70 degrees
- The measure of angle PQS is 53 degrees
- The measure of angle RPS is 35 degrees
- The measure of angle PSQ is 53 degrees
The given parameters are:
![\mathbf{\angle PQR = 106}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20PQR%20%3D%20106%7D)
![\mathbf{\angle QSR = 49}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20QSR%20%3D%2049%7D)
![\mathbf{\angle PRS = 35}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20PRS%20%3D%2035%7D)
<u>(a) Find QRS</u>
This is calculated as:
![\mathbf{\angle QRS = 2 \times \angle PRS }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20QRS%20%3D%202%20%5Ctimes%20%5Cangle%20PRS%20%7D)
So, we have:
![\mathbf{\angle QRS = 2 \times 35}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20QRS%20%3D%202%20%5Ctimes%2035%7D)
![\mathbf{\angle QRS = 70}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20QRS%20%3D%2070%7D)
Hence, the measure of angle QRS is 70 degrees
<u>(b) Find PQS</u>
This is calculated as:
![\mathbf{\angle PQS = \frac 12 \times \angle PQR }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20PQS%20%3D%20%5Cfrac%2012%20%5Ctimes%20%5Cangle%20PQR%20%7D)
So, we have:
![\mathbf{\angle PQS = \frac 12 \times 106}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20PQS%20%3D%20%5Cfrac%2012%20%5Ctimes%20106%7D)
![\mathbf{\angle PQS = 53}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20PQS%20%3D%2053%7D)
Hence, the measure of angle PQS is 53 degrees
<u>(c) Find RPS</u>
This is calculated as:
![\mathbf{\angle RPS = \angle PRQ }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20RPS%20%3D%20%5Cangle%20PRQ%20%7D)
Where:
![\mathbf{\angle PRQ = \angle PRS = 35}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20PRQ%20%20%3D%20%5Cangle%20PRS%20%3D%2035%7D)
So, we have:
![\mathbf{\angle RPS = 35}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20RPS%20%20%3D%2035%7D)
Hence, the measure of angle RPS is 35 degrees
<u>(d) Find PSQ</u>
This is calculated as:
![\mathbf{\angle PSQ =\frac 12 \times \angle PQR }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20PSQ%20%3D%5Cfrac%2012%20%5Ctimes%20%5Cangle%20PQR%20%7D)
Where:
![\mathbf{\angle PSQ =\frac 12 \times \angle 106}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20PSQ%20%3D%5Cfrac%2012%20%5Ctimes%20%5Cangle%20106%7D)
So, we have:
![\mathbf{\angle PSQ =53}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cangle%20PSQ%20%3D53%7D)
Hence, the measure of angle PSQ is 53 degrees
Read more about angles in a parallelogram at:
brainly.com/question/12186483
Step-by-step explanation:
a) one solution
x=30
b) no solution 0=0
c) no solution
0≠-21
The answer is: 75,000 mg
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Explanation:
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Note: 1000 mg = 1g ; is an exact value conversion;
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Convert 75 grams, or "75 g", into "milligrams" (mg).
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75 g * (1,000 mg/1g) = ? mg ?
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The "g" units cancel ; and we are left with:
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[(75 * 1,000 mg)] / (1) = (75 * 1,000 mg) = 75,000 mg
One thirtieth of an hour more because he spent twenty four thirtieths of an hour on monday and twenty five thirtieths of an hour on tuesday