Question

two adjacent angles of a parallelogram are in the ratio 5:2: . find all the angles of the parallelogram​

Answer 1

Given:- two adjacent angles of parallelogram are 5:2.

Solution :-

As we know that sum of adjacent angles of parallelogram is 180°.

Now, let the ratio be x.

• 1st angle = 5x
• 2nd angle = 2x

According to question,

⇒ 5x + 2x = 180

⇒ 7x = 180

⇒ x= 180/7

So,

• 1st angle = 5x = 180/7 × 5 = 128.2°

• 2nd angle = 2x = 2×180/7 = 51.4°

Because opposite angles of parallelogram are equal,

• 3rd angle = 128.2°

• 4th angle = 51.4°

Answer 2

Answer:

Given :-

• Two adjacent angles of a parallelogram are in the ratio of 5 : 2.

To Find :-

• What is the all angles of the parallelogram.

Solution :-

Let, the first angles be 5x

And, the second angles will be 2x

As we know that,

★ Sum of all angles = 180° ★

According to the question by using the formula we get,

⇒ $\sf 5x + 2x =\: 180^{\circ}$

⇒ $\sf 7x =\: 180^{\circ}$

⇒ $\sf x =\: \dfrac{\cancel{180^{\circ}}}{\cancel{7}}$

➠ $\sf\bold{\red{x =\: 25.7^{\circ}}}$

Hence, the required angles are,

✧ First angles = 5x = 5(25.7°) = 128.5°

✧ Second angles = 2(25.7°) = 51.4°

As we know that, opposite angles in a parallelogram is equal.

$\therefore$ The all angles of a parallelogram is 128.5°, 51.4°, 128.5° and 51.4°.