Question

Two adjacent angles of a parallelogram are 2x and 3x. The measures of these angles are?

1)30,60
2)30,90
3)36,72
4)72,108​

Answer 1

Answer :

• The measures of these angles are 72⁰ , 108⁰

Given :

• Two adjacent angles of a parallelogram are 2x and 3x

To find :

• Measure of these angles are

Solution :

Given

Two adjacent angles of a parallelogram are

• 2x and 3x

We know that

• Sum of adjacent angles of a parallelogram is 180⁰

According to question :

➟ 2x + 3x = 180⁰

➟ 5x = 180⁰

➟ x = 180⁰/5

➟ x = 36⁰

Finding the measure of angles :

➟ 2x

➟ 2(36⁰)

➟ 72⁰

➟ 3x

➟ 3(36⁰)

➟ 108⁰

Hence , The measures of these angles are 72⁰ , 108⁰

Verification :

➟ 2x + 3x = 180⁰

➟ 2(36⁰) + 3(36⁰) = 180⁰

➟ 72⁰ + 108⁰ = 180⁰

➟ 180⁰ = 180⁰

LHS = RHS

Hence , Verified.

Answer 2

Given :-

• Two adjacent angles of a parallelogram are 2x and 3x.

To Find :-

• Measure of these angles.  

Solution :-

⠀

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❍ To calculate the measure of those angles we must know that ::  

• Adjacent angles of a parallelogram are supplementary.  

• Sum of supplementary angles is 180°.

Finding the value of x :-

• As the adjacent angles of parallelogram are supplementary we can form an equation :

⇝ 3x + 2x = 180°

⇝ 5x = 180°

⇝ x = 180°/5

⇝ x = 36°

Finding the angles :-

⇝  2x = 2 × 36° = 72°

⇝ 3x = 3 × 36°  = 108°

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• Henceforth, measures of the angles are 72° and 108°.