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).

Explanation:

Step1: Set up angle sum equation

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

Step2: Simplify right side

$11x - 31 = 8x + 17$

Step3: Solve for x

$3x = 48 \implies x = 16$

Step4: Calculate $m\angle ABF$

$m\angle ABF = 6(16) + 26 = 122$

Answer:

122°