Question

Find the measure of each angle of a parallelogram if the larger angle of a parallelogram is 30° less than twice the smaller angle

Answer 1

Step-by-step explanation:

Let , the smaller angle of ||gm = x

then , larger angle of ||gm = 2x - 30°

As we know that the sum of two adjacent angles of ||gm is equal to 180°

So,

x + 2x - 30° = 180°

→ 3x - 30° = 180°

→ 3x = 180° + 30°

→ 3x = 210°

→ x = 210°/3

→ x = 70°

So, the larger angle = 2x - 30 = 140 - 30 = 110°

and the smaller angle = x = 70°

Answer 2

Given :

• the larger angle of a parallelogram is 30° less than twice the smaller angle

To Find :

• Measure of each angle of the parallelogram.

Solution :

Sun of two adjacent angles of a parallelogram is equal to 180°

Let the smaller angle be x

Let the larger angle be 2x - 30°

According to the question :

⟶ x + 2x - 30° = 180°

⟶ 3x - 30 = 180°

⟶ 3x = 180° + 30°

⟶ 3x = 210

⟶ x = 210/3

⟶ x = 70

Therefore :

Smaller angle = x = 70°

Larger angle = 2x - 30° = 2(70) - 30 = 140 - 30 = 110°

So, all the angles of the parallelogram are 70° , 110° , 70° and 110°

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