Question

in the given figure PQRS IS a parallelogram. find the measure of angle spr and angle pqr​

Answer 1

Step-by-step explanation:

spr = 60°

pqr=120°

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°

∠PQR  = 60° and ∠SPR  = 60°

(Figure was incomplete and complete figure has been attached)

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