Question

What value of x will make angles AOB and BOC a linear pair

Answer 1

Step-by-step explanation:

AOB + BOC = 180° (linear pair)

3x+30 + 2x-20 = 180°

5x+10 = 180°

5x = 170

x = 170/5

x = 34

The two angles are

3x + 30

= 3(34) + 30

=132°

2x - 20

= 2(34)-20

=48°

Hope it helps:)

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:}}}}$

x is 34 and the angles are 132° and 48°.

$\mathfrak{\large{\underline{\underline{Step-by-step\:explanation:}}}}$

$\textsf{\underline{\underline{Given :}}}$

$\textsf{Measure of}$ $\angle$ AOB = $\textsf{(3x+30)}$

$\textsf{Measure of}$ $\angle$ BOC = $\textsf{(2x-20)}$

$\textsf{\underline{\underline{To find :}}}$

$\textsf{Value of x}$

$\textsf{\underline{\underline{Solution :}}}$

Linear pair of angles are the two angles who are when added sum up 180°.

★ $\green{\boxed{\green{\boxed{\red{\sf{3x + 3x + (2x - 20) = 180}}}}}}$

$\sf{\longrightarrow} \: 3x + 30 + (2x - 20) = 180 \\ \\ \sf{\longrightarrow} \: 3x + 2x + 30 - 20 = 180 \\ \\ \sf{\longrightarrow} \: 5x + 10 = 180 \\ \\ \sf{\longrightarrow} \: 5x = 180 - 10 \\ \\ \sf{\longrightarrow} \: 5x = 170 \\ \\ \sf{\longrightarrow} \: x = \frac{170}{5} \\ \\ \sf{\longrightarrow} \: x = 34$

$\rule{300}{1.5}$

★ $\textbf{\small{\underline{Value of (3x + 30)}}}$

$\sf{\longrightarrow} \: 3(34) + 30 \\ \sf{\longrightarrow} \: 102 + 30 \\\sf{\longrightarrow} \: 132$

$\textsf{Measure of}$ $\angle$ AOB = $\textsf{132}$°

$\rule{300}{1.5}$

★ $\textbf{\small{\underline{Value of (2x - 20)}}}$

$\sf{\longrightarrow} \: 2(34) - 20 \\ \sf{\longrightarrow} \: 68 - 20 \\ \sf{\longrightarrow} \: 48$

$\textsf{Measure of}$ $\angle$ BOC = $\textsf{48}$°

$\therefore$ x is 34 and the angles are 132° and 48°.