Question

If m□ebd=4x-8 and m□ebc=5x+20,find the value of x and m□ebc

Answer 1

The value of x is 18.67° and m∠ebc = 113.33°

Here is the correct question:

If m∠EBD= 4x - 8 and m∠EBC= 5x + 20, find the value of x and m∠EBC.

The diagram that completes the question is shown in the attachment below:

In the diagram, we can observe that dbc is a straight line.

Also ∠ebd and ∠ebc are the angles on the straight line

Since the sum of angles on a straight line is equal to 180°, then we can write that

∠ebd +  ∠ebc = 180°

From the question

m∠ebd = 4x - 8 and  m∠ebc = 5x + 20

∴ 4x - 8 + 5x + 20 = 180°

Solving the linear equation

$4x - 8 + 5x + 20 = 180^{o}$

Then,

$4x + 5x + 20 -8= 180^{o}$

$9x + 12 = 180$

$9x = 180 - 12$

$9x = 168$

Now, divide both sides by 9

$\frac{9x}{9}=\frac{168}{9}$

∴ $x = 18\frac{2}{3}^{o} \ or \ 18.67^{o}$

∴ x ≅ 18.67°

For the value of m∠ebc

Since, m∠ebc = 5x + 20

∴ m∠ebc = $5(18\frac{2}{3}) + 20$

m∠ebc $= 5 (\frac{56}{3} ) +20$

m∠ebc = $\frac{280}{3}+20$

m∠ebc = 93.33 + 20

m∠ebc = 113.33°

Hence, the value of x is 18.67° and m∠ebc = 113.33°

Learn more here: https://brainly.com/question/11042147