Question

An angle measures 4.6° less than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

Answer:

The two angles are,

87.7° and 92.3°

Step-by-step explanation:

Question,

To find an angle and it's supplementary angle.

Let,

The supplementary angle be = x

So, the angle given is = x - 4.6

As we know,

When two angles added gives 180°, then those angles are called supplementary angles.

Therefore solution,

By the problem,

=> x + (x - 4.6) = 180

• [On adding like terms x]

=> 2x - 4.6 = 180

• [Putting - 4.6 to other side of equal to which converts to 4.6]

=> 2x = 180 + 4.6 = 184.6

• [On dividing 2 on both sides]

$= > \frac{2x}{2} = \frac{184.6}{2}$

• [On Simplification]

=> x = 92.3

Result:

So, the supplementary angle is = 92.3° (Ans)(ii)

And, it's required angle is = 180° - 92.3° = 87.7° (Ans)(i)

Answer 2

Supplementary Angles :

• If the sum of the measures of two angles is 180°, then the angles are called supplementary angles and each angle is called a supplement of the other.

⠀

Given :

• An angle measures 4.6° less than the measure of its supplementary angle.

⠀

To Find :

• The measure of each angle.

⠀

Solution :

• Let's assume the one of the supplementary angle as "x" and the other angle as (x + 4.6)° .

Now,

According to the Question :

$\begin{gathered}\\ \sf x + (x - 4.6) {}^{ \circ} = 180{}^{ \circ} \\ \\ \dashrightarrow \: \sf x + x - 4.6{}^{ \circ} = 180{}^{ \circ} \\ \\ \sf \: \dashrightarrow 2x - 4.6{}^{ \circ} = 180{}^{ \circ} \: \: \: \: \\ \\ \dashrightarrow \sf \: 2x = 180{}^{ \circ} + 4.6{}^{ \circ} \\ \\ \dashrightarrow \sf \: 2x = 184.6{}^{ \circ} \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow \: \sf \: x = \frac{184.6 {}^{ \circ} }{2} \: \: \: \: \: \\ \\ \dashrightarrow \: \sf \: x = 92.3 {}^{ \circ} \: \: \: \: \: \\ \\\end{gathered}$

Therefore,

• One angle = 92.3°
• Other angle = 180° – 92.3° = 87.7°

⠀

Hence,

• The measure of the two angles are 92.3° and 87.7° .