Question

in the following figure pqrs is a parallelogram find the measure of angle SPR and angle pqr ​

Answer 1

Answer:

60°

Step-by-step explanation:

b/c angle PRQ is 60°

So angle PRQ=angle SPR

60°=angle SPR

So triangle PRS is equilateral trangle....

Answer 2

Measure of ∠SPR  and  ∠PQR are 60° each in Parallelogram PQRS

Given:

• PQRS is a parallelogram
• m∠PRQ = 60°
• m∠PST = 120° ( exterior angle of ∠PSR)

To Find:

• Measure of ∠SPR
• Measure of ∠PQR

Solution:

• Sum of angles forming Linear pair is 180°
• Opposite sides of parallelogram are parallel
• Opposite angles of parallelogram are Equal in measure
• Adjacent angles of Parallelogram are supplementary

Step 1:

RST is a starlight line Hence ∠PST and ∠PSR form a linear pair

∠PST + ∠PSR = 180°

Step 2:

Substitute ∠PST  = 120° and solve for ∠PSR

120° +  ∠PSR = 180°

∠PSR  = 60°

Step 3:

Opposite angles of parallelogram are equal

∠PQR  = ∠PSR  

∠PQR  = 60°

Step 4:

PS || QR and PR is transversal Hence alternate interior angles are equal

∠SPR  = ∠PRQ

∠SPR  = 60°

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