Question

□PQRS is parallelogram. if measure of angle P=60°, then find the measures of all angles of a parallelogram​

Answer 1

We know that, sum of supplementary angle is equal to 180o. And also, opposite angles ∠P and ∠R are equal in parallelogram. Therefore, the other three angles of parallelograms are 60o, 120o and 120o

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Answer 2

Step-by-step explanation:

PQRS is a parallelogram.

∠P = 60°

In a parallelogram, opposite angles are equal.

So, ∠P = ∠R

Measure of ∠R = 60°

We know that adjacent angles in parallelogram are supplementary, which means their sum is 180°.

Adjecent angles are ∠P and ∠S, ∠Q and ∠R.

$\longrightarrow$ ∠P + ∠S = 180°

$\longrightarrow$ ∠S + 60° = 180°

$\longrightarrow$ ∠S = 180° - 60°

$\longrightarrow$ ∠S = 120°

∠S is opposite to ∠Q,

$\longrightarrow$ ∠S = ∠Q

$\longrightarrow$ ∠Q = 120°

Therefore, angles of the parallelogram are :

• ∠P = 60°
• ∠Q = 120°
• ∠R = 60°
• ∠S = 120°

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★ Verification:

Verifying by the angle sum property of a parallelogram.

Sum of all angles in a parallelogram is 360°.

$\longrightarrow$ ∠P + ∠Q + ∠R + ∠S

$\longrightarrow$ 60° + 120° + 60° + 120°

$\longrightarrow$ 120° + 240°

$\longrightarrow$ 360°

Hence verified.