Question

two angles are complementary the larger angle is 3degree less than twice the measure of the smaller angle find the measure of each angle​

Answer 1

Correct Question:

Two angles are complementary. The larger angle is 3 degrees less than twice the measure of the smaller angle. Find the measure of each angle.

Solution:

The basic concept to be kept in mind is that:

The sum of two complementary angles is 90°. Therefore the constituent complements will both have measures smaller than 90° and will also add upto 90°.

Statement: The larger angle is 3 degrees less than twice the measure of the smaller angle.

Let the smaller angle be x. This means that the larger angle is 3 degrees less than 2x.

Larger angle = 2x - 3

As said before, sum of two complementary angles is 90°.

Forming an equation:

$\sf{x+2x-3=90^o}$

$\sf{3x-3=90^o}$

$\sf{3x=90+3}$

$\sf{3x=93}$

$\sf{x=\dfrac{93}{3}}$

$\sf{x=31}$

Therefore,

The measure of the smaller angle = x = 31°

The measure of the larger angle = 2x - 3

= (2 x 31) - 3

= 62 - 3

= 59°

So, the complementary angles are 31° and 59°.

⇒ Verification:

LHS:

= 31 + 59

= 90

RHS:

= 90

LHS = RHS

Hence verified!

Knowledge Bytes:

⇒ Complementary angles:

Those angles that add upto 90° are known as complementary angles. These angles are complement to each other. Together, they form a right angle.

⇒ Supplementary angles:

Those angles that add upto 180° are known as supplementary angles. These angles are supplement to each other. Together, they form a straight angle.

Answer 2

Answer:

$\huge \underline \mathfrak \red{Correct \: Question}$

Two angles are complementary. The larger angle is 3 degrees less than twice the measure of the smaller angle. Find the measure of each angle.

$\huge \underline \mathfrak \red{Solution}$

The basic concept to be kept in mind is that:

The sum of two complementary angles is 90°. Therefore the constituent complements will both have measures smaller than 90° and will also add upto 90°.

Statement: The larger angle is 3 degrees less than twice the measure of the smaller angle.

Let the smaller angle be x. This means that the larger angle is 3 degrees less than 2x.

Larger angle = 2x - 3

As said before, sum of two complementary angles is 90°.

Forming an equation:

x+2x−3=90

3x−3=90

3x=90+3

3x=93

x= 93/3

x=31

Therefore,

The measure of the smaller angle = x = 31°

The measure of the larger angle = 2x - 3

= (2 x 31) - 3

= 62 - 3

= 59°

So, the complementary angles are 31° and 59°.

⇒ Verification:

LHS:

= 31 + 59

= 90

RHS:

= 90

LHS = RHS

Hence verified!

Knowledge Bytes:

⇒ Complementary angles:

Those angles that add upto 90° are known as complementary angles. These angles are complement to each other. Together, they form a right angle.

⇒ Supplementary angles:

Those angles that add upto 180° are known as supplementary angles. These angles are supplement to each other. Together, they form a straight angle.