Question

Two adjacent angles of parallelogram are x° and (3x - 20)° find the measure of angle (3x - 20)​

Answer 1

Answer:

The value of x = 75°.

Given :

The two adjacent angles of a parallelogram are :

The first angle = (3x – 20°).

The second angle = (50° – x).

To Find :

The value of x.

Solution :

Given,

The two adjacent angels of a parallelogram are (3x – 20°) and (50° – x).

We know that,

The measure of the two adjacent angles is supplementary angle.

Supplementary angle = 180°

That means,

The measure of the two adjacent angles is 180°

⇒ (3x – 20°) + (50° – x) = 180°

⇒ 3x – 20° + 50° – x = 180°

⇒ 3x – x + 50° – 20° = 180°

⇒ 2x + 30° = 180°

⇒ 2x = 180° – 30°

⇒ 2x = 150°

⇒ x = 150° / 2

⇒ x = 75°

Hence,

The value of x is 75°

Verification :

We know that,

The measure of the two adjacent angles is 180°

That means,

⇒ (3x – 20°) + (50° – x) = 180°

The value of x = 75°

⇒ [ 3 (75°) – 20° ] + [ 50° – (75°) ] = 180°

⇒ [ 225° – 20° ] + [ – 25° ] = 180°

⇒ [ 205° ] + [ – 25° ] = 180°

⇒ 205° – 25° = 180°

⇒ 180° = 180°

Step-by-step explanation:

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