Question

Two adjacent angles on a straight line are (3x-2)⁰ and 4(x+7)⁰ . Find (i) the value of x (ii) the measure of each angle​

Answer 1

Answer:

$\large\underline{\underline{\maltese{\color{pink}{\pmb{\sf{Given:-}}}}}}$

Adjacent Angles in Straight Line are :

• (3x - 2) °
• 4(x + 7) °

$\large\underline{\underline{\maltese{\color{green}{\pmb{\sf{\: To \: Find:-}}}}}}$

• Value of x?
• Measure of each angle?

$\large\underline{\underline{\maltese{\color{red}{\pmb{\sf{Solution:-}}}}}}$

We Know that Sum of adjacent Angles = 180°

${ \longrightarrow{ \sf{3x - 2 + 4(x + 7) = 180}}}$

${ \longrightarrow{ \sf{3x - 2 + 4x + 28 = 180}}}$

${ \longrightarrow{ \sf{7x + 26 = 180}}}$

${ \longrightarrow{ \sf{7x = 180 - 26}}}$

${ \longrightarrow{ \sf{7x = 154}}}$

${ \longrightarrow{ \sf{ \pmb{x = 22}}}}$

Finding Angles:

➡️ 3x - 2 = 3(22) - 2 = 66 - 2 = 64°

➡️ 4x + 28 = 4(22) + 28 = 88 + 28 = 116°

$\large\underline{\underline{\maltese{\color{blue}{\pmb{\sf{Final \: Answer : -}}}}}}$

The Measure of x is 22°

The Angles are 64° , 116°

Answer 2

Answer:

Given that x

o

and (2x−27)

o

are adjacent angles on a straight line.

Now, x

o

+(2x−27)

o

=180

o

...(Since adjacent angles on a straight line =180

o

)

⇒3x=180+27

⇒3x=207

⇒x=

3

207

⇒x=69

The ajacent angles are as follows:

x

o

=69

o

And, 2x−27

o

=2×69−27=138−27=111

o

Step-by-step explanation:

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