Question

Two complementey angles are in the ratio2:3 find the measure of an angle

Answer 1

Given :-

• Two complementary angles are in the ratio of 2 : 3.

To Find :-

• What is the measure of an angle.

Solution :-

Let,

◘ First angle = 2x

◘ Second angle = 3x

According to the question,

⇒ 2x + 3x = 90°

⇒ 5x = 90°

⇒ x = 90°/5

➠ x = 18°

Hence, the required angles are :

➲ First angle :

↦ 2x

↦ 2(18°)

↦ 2 × 18°

➦ 36°

➲ Second angle :

↦ 3x

↦ 3(18°)

↦ 3 × 18°

➦ 54°

∴ The measure of an angle is 36° and 54° respectively.

VERIFICATION :-

⇒ 2x + 3x = 90°

By putting x = 18° we get,

⇒ 2(18°) + 3(18°) = 90°

⇒ 36° + 54° = 90°

➤ 90° = 90°

Hence, Verified.

Answer 2

$\huge\sf{\underline{Given:}}$

• Two complementary angles are in ratio 2:3.

$\huge\sf{\underline{To \: Find:}}$

• What is the measure of the angle?

$\huge\sf{\underline{Solution:}}$

Let,

$\small\implies\sf{First \: angle = 2x}$

$\small\implies\sf{Second \: angle = 2x}$

$\huge\sf{\underline{According \: to \: question:}}$

$\implies\sf{2x+3x = 90°}$

$\implies\sf{5x = 90°}$

$\implies\sf{x = 90°/5}$

$\implies\sf\fbox{\green{x = 18°}}$

Hence, the required angles are:-

$\sf{☞ \: First \: angle = 2x}$

$\: { \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2×18°}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {36°}$

$\sf{☞ \: Second \: angle = 3x}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3 \times 18°$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 54°$

∴ Measure of angles are 36° and 54° respectively.

$\huge\sf{\underline{\red{Verification:}}}$

$\small\implies\sf{2x+3x = 90°}$

$\small\implies\sf{2(18°)+3(18°) = 90°}$

$\small\implies\sf{36°+54°=90°}$

$\small\implies\sf\fbox{\purple{90°=90°}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf\fbox{\green{Verified}}$