Question

Suppose $m\angle 3=3x+5$and $m\angle 4=6x+13$. Find the value of x.

Short answer

The value ofx is18.

Step-by-step solution

Step 1. Observe the diagram.

$m\angle 3=3x+5$ … (i)

$m\angle 4=6x+13$ ... (ii)

From the diagram,

$m\angle 3+m\angle 4=180°$

Step 2. Show the calculation.

Here, $m\angle 3+m\angle 4=180°$.

By substituting the value from equation (i) and (ii),

$\left(3x+5\right)+\left(6x+13\right)=180$

$9x+18=180$

$9x=180-18$

$9x=162$

That implies,

x=18

Putting the value of x in equation (i),

$m\angle 3=3x+5$

$=\left(3\times 18\right)+5$

$=54+5$

$=59$

Putting the value of x in equation (ii),

$m\angle 4=6x+13$

$=\left(6\times 18\right)+13$

$=108+13$

$=121$

Step 3. State the conclusion.

Therefore, the value of xis 18.