Question

If two complememtary angles are in the ratio 13:5, then the angles are:

Answer 1

$\LARGE{ \underline{ \purple{ \sf{Required \: answer:}}}}$

Complementary angles are the angles which add upto 90° or their sum is 90°. They need not to be adjacent angles necessarily.

Given:

• Ratio of the complementary angles is 13 : 5

━━━━━━━━━━━━━━━━━━━━

Let the angles be 13x and 5x.

Then,

⇛ 13x + 5x = 90°

⇛ 18x = 90°

⇛ x = 90° / 18 = 5°

The measure of the angles are:

• 13x = 13(5°) = 65°
• 5x = 5(5°) = 25°

And we are done !!

Answer 2

$\bf\large\red{\underline{given : }}$

• Two angles are complementary.
• They are in the ratio 13:5.

$\\ \bf\large\red{\underline{to \: find : }}$

• The angles.

$\\ \bf\large\red{\underline{to \: know : }}$

• The complementary angles have the sum 90°. They must be adjecent to each other.

$\\ \bf\large\red{\underline{solution : }}$

Let us consider the two angles as 13x and 5x.

Sum of these angles is 90°.

⇒ 13x + 5x = 90

⇒ 18x = 90

⇒ x = 5

☛Angles are,

➜ 13x

⇒ 13(5)

⇒ 65°

➜ 5x

⇒ 5(5)

⇒ 25°

∴ Angles are 65° and 25°.

To remember :-

• Supplementary angles have the sum 180°. They must be adjecent. They are also known as linear pair.