Question

use the diagram to the left to answer questions 9 and 10. 9. if (mangle abf=(6x + 26)^{circ}), (mangle ebf=(2x - 9)^{circ}), and (mangle abe=(11x - 31)^{circ}), find (mangle abf). 10. if (overrightarrow{bd}) bisects (angle cbe), (overrightarrow{bc}perpoverrightarrow{ba}), (mangle cbd=(3x + 25)^{circ}), and (mangle dbe=(7x - 19)^{circ}), find (mangle abd).

Explanation:

Step1: Set up equation for question 9

$m\angle ABF + m\angle EBF=m\angle ABE$, so $(6x + 26)+(2x - 9)=11x - 31$.

Step2: Simplify equation

$8x+17 = 11x - 31$.

Step3: Solve for x

$3x=48$, $x = 16$.

Step4: Find $m\angle ABF$

$m\angle ABF=6x + 26=6\times16+26 = 122^{\circ}$.

Answer:

$122^{\circ}$