Question

The two angles of a parallelogram are in the ratio 5:13. If the bigger angle is halved then what will be the ratio of new parallelogram obtained?

Answer 1

The ratio of angles of new parallelogram obtained will be 23:13.

Step-by-step explanation:

The given ratio of the two angles of a parallelogram = 5:13

Let’s assume one of the angle be “ 5x° ” and the other angle be “ 13x° ”.

Step 1:

We know that the opposite angles of a parallelogram are equal and the sum of adjacent angles is equal to 180°.  

From the given ratio we can conclude that the given angles are the adjacent angles, therefore, we get the eq. as,

5x + 13x = 180°

⇒ 18x = 180°

⇒ x = 10°

∴ 5x = 5 * 10° = 50°

And,

13x = 13 * 10° = 130°

Step 2:

Now,  

When the bigger angle (13x) is halved i.e., $\frac{130}{2}$ = 65°

The smaller angle (5x) will be = 180° - 65° = 115°

Thus,  

The ratio of the angles of new parallelogram will be,

= 115 : 65

= 23 : 13

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Answer 2

Dear Student,

◆ Answer -

Ratio of new parallelogram = 13 : 23.

● Explanation -

Let x be a common multiple such that two adjacent angles be 5x and 13x.

Sum of two adjacent angles of parallelogram is 180°.

5x + 13x = 180

18x = 180

x = 10°

So bigger angle is -

13x = 13 × 10 = 130°

Given that bigger angle is halved. 130/2 = 65°.

Other angle now will be 180-65 = 115°.

So ratio of new parallelogram will be 65° : 115° = 13 : 23.

Thanks dear. Hope this helps you..