Question

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​

Answer 1

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:

$\mathbf{\angle PQR = 106}$

$\mathbf{\angle QSR = 49}$

$\mathbf{\angle PRS = 35}$

(a) Find QRS

This is calculated as:

$\mathbf{\angle QRS = 2 \times \angle PRS }$

So, we have:

$\mathbf{\angle QRS = 2 \times 35}$

$\mathbf{\angle QRS = 70}$

Hence, the measure of angle QRS is 70 degrees

(b) Find PQS

This is calculated as:

$\mathbf{\angle PQS = \frac 12 \times \angle PQR }$

So, we have:

$\mathbf{\angle PQS = \frac 12 \times 106}$

$\mathbf{\angle PQS = 53}$

Hence, the measure of angle PQS is 53 degrees

(c) Find RPS

This is calculated as:

$\mathbf{\angle RPS = \angle PRQ }$

Where:

$\mathbf{\angle PRQ = \angle PRS = 35}$

So, we have:

$\mathbf{\angle RPS = 35}$

Hence, the measure of angle RPS is 35 degrees

(d) Find PSQ

This is calculated as:

$\mathbf{\angle PSQ =\frac 12 \times \angle PQR }$

Where:

$\mathbf{\angle PSQ =\frac 12 \times \angle 106}$

So, we have:

$\mathbf{\angle PSQ =53}$

Hence, the measure of angle PSQ is 53 degrees

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