Given PQ = 24
PS = 19
PR = 42
TQ = 10
m<PQR = 106°
m<QSR = 49°
m<PRS = 35°
find m<QRS, m<PQS, m<RPS and m<PSQ
Answers
The shape PQRS is a parallelogram
The measure of angle QRS is 70 degreesThe measure of angle PQS is 53 degreesThe measure of angle RPS is 35 degreesThe measure of angle PSQ is 53 degreesThe given parameters are:
[tex]\mathbf{\angle PQR = 106}[/tex]
[tex]\mathbf{\angle QSR = 49}[/tex]
[tex]\mathbf{\angle PRS = 35}[/tex]
(a) Find QRS
This is calculated as:
[tex]\mathbf{\angle QRS = 2 \times \angle PRS }[/tex]
So, we have:
[tex]\mathbf{\angle QRS = 2 \times 35}[/tex]
[tex]\mathbf{\angle QRS = 70}[/tex]
Hence, the measure of angle QRS is 70 degrees
(b) Find PQS
This is calculated as:
[tex]\mathbf{\angle PQS = \frac 12 \times \angle PQR }[/tex]
So, we have:
[tex]\mathbf{\angle PQS = \frac 12 \times 106}[/tex]
[tex]\mathbf{\angle PQS = 53}[/tex]
Hence, the measure of angle PQS is 53 degrees
(c) Find RPS
This is calculated as:
[tex]\mathbf{\angle RPS = \angle PRQ }[/tex]
Where:
[tex]\mathbf{\angle PRQ = \angle PRS = 35}[/tex]
So, we have:
[tex]\mathbf{\angle RPS = 35}[/tex]
Hence, the measure of angle RPS is 35 degrees
(d) Find PSQ
This is calculated as:
[tex]\mathbf{\angle PSQ =\frac 12 \times \angle PQR }[/tex]
Where:
[tex]\mathbf{\angle PSQ =\frac 12 \times \angle 106}[/tex]
So, we have:
[tex]\mathbf{\angle PSQ =53}[/tex]
Hence, the measure of angle PSQ is 53 degrees
Read more about angles in a parallelogram at:
https://brainly.com/question/12186483
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