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KATRIN_1 [288]
3 years ago
5

Given PQ = 24

Mathematics
1 answer:
Verdich [7]3 years ago
7 0

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}

<u>(a) Find QRS</u>

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

<u>(b) Find PQS</u>

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

<u>(c) Find RPS</u>

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

<u>(d) Find PSQ</u>

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

Read more about angles in a parallelogram at:

brainly.com/question/12186483

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