If m∠EBD= 4x - 8 and m∠EBC= 5x + 20, find the value of x and m∠EBC.
Accepted Solution
A:
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 [tex]4x - 8 + 5x + 20 = 180^{o}[/tex]Then, [tex]4x + 5x + 20 -8= 180^{o}[/tex][tex]9x + 12 = 180[/tex][tex]9x = 180 - 12[/tex][tex]9x = 168[/tex]Now, divide both sides by 9 [tex]\frac{9x}{9}=\frac{168}{9}[/tex]∴ [tex]x = 18\frac{2}{3}^{o} \ or \ 18.67^{o}[/tex]∴ x ≅ 18.67°For the value of m∠ebcSince, m∠ebc = 5x + 20∴ m∠ebc = [tex]5(18\frac{2}{3}) + 20[/tex]m∠ebc [tex]= 5 (\frac{56}{3} ) +20[/tex]m∠ebc = [tex]\frac{280}{3}+20[/tex]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: