Question

1 point
Q26 Two supplementary angles
differ by 32°. Find the smaller angle.
O 106°
O 180°
O 42°
O 740​

Answer 1

Given:

✰ Two supplementary angles differ by 32°

To find:

✠ The smaller angle.

Solution:

Supplementary angles:

Two angles are said to be supplementary if the sum of their ages is 180° and each one of them is called the supplement of the other.

Here in this question, first we will assume that the two angles are x and y, then we will form the equation① because we know the sum of the supplementary angle is 180°. We are given that two supply entry angles differ by 32°, that means when we subtract these angles their difference is equal to 32°. So, here we will form and equation②, that is, the value of the bigger angle. Afterwards, we will substitute the value of second equation in eq① to get the value of smaller angle x.

Let's find out...♪

Let the two supplementary angles be x and y and,

x be the smaller supplementary angle.

Sum of supplementary angles is 108°

➛ x + y = 180° ...①

Now, two supplementary angles differ by 32°

➛ y - x = 32°

➛ y = x + 32 ...②

Substituting the value of eq② in eq①

➛ x + (x + 32°) = 180°

➛ 2x + 32° = 180°

➛ 2x = 180° - 32°

➛ 2x = 148

➛ x = 148/2

➛ x = 74°

∴ The smaller angle = 74°

What if we need to find bigger angle also?

Substitute the value of x in eq①

➛ x + y = 180°

➛ 74° + y = 180°

➛ y = 180° - 74°

➛ y = 106°

∴ The bigger angle = 106°

_______________________________

Answer 2

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

• Two angles differ by 32° .

‎

$\large\sf\underline{To\:find\::}$

• Smaller angle .

‎

$\large\sf\underline{Assumption\::}$

Let :

• The smaller angle be x° .

Since the two angles differ by 32° .

• The bigger angle be ( x + 32 )° .

‎

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

We know ,

${\sf{{\orange{Sum\:of\: supplementary\:angles\:=\:180°}}}}$

So here ,

$\sf\: Smaller\:angle+Larger\: angle=180°$

• Substituting the value we had assumed earlier .

$\sf\implies\:x+(x+32)=180°$

$\sf\implies\:x+x+32=180°$

$\sf\implies\:2x+32=180°$

• Transposing 32 to the other side .

Since 32 is ${\sf{{\pink{+}}}}$ in LHS , when we transpose it to RHS it becomes ${\sf{{\pink{-}}}}$

$\sf\implies\:2x=180-32$

$\sf\implies\:2x=148$

• Transposing 2 to the other side

Since ${\sf{{\pink{×}}}}$ sign lies between 2 and x in LHS , when we transpose 2 to RHS it becomes ${\sf{{\pink{÷}}}}$

$\sf\implies\:x=\frac{148}{2}$

$\large{\mathfrak\purple{\implies\:x=74}}$

‎

Now as we got the value for x let's substitute that value in the assumed values :

$\sf\:Smaller\:angle\:=x$

$\large{\mathfrak\red{\implies\:Smaller\:angle=74°}}$

________________________⊛

$\sf\:Larger\:angle\:=(x+32)°$

$\sf\implies\:Larger\:angle\:=(74+32)°$

$\large{\mathfrak\red{\implies\:Larger\:angle=106°}}$

‎

‎

$\small\rm\purple\star\:\underline{Verifying\:my\:answer\::}$

From the properties of triangle we know that ,

$\dag\:\underline{\sf Sum\:of\: Supplementary\:angles\:=\:180°}$

$\sf\:Larger\: angle\:+Smaller\:angle=180°$

So let's substitute the value of the smaller and larger angles that we got :

$\sf\implies\:106°+74°=180°$

‎ $\sf\implies\:180°=180°$

$\small\fbox\green{[\:Hence\: Verified\:]}$

‎

!! Hope it helps !!