Final answer:
After solving the equation 5x + 10 = 8x - 17, we find x = 9. The measures of angles ZAXB and ZBXC are both 55°, thus XB and ZAXC form an acute angle since each is less than 90°.
Step-by-step explanation:
To find the value of x, set the measures of angles ZAXB and ZBXC equal to each other since XB bisects ZAXC:
5x + 10 = 8x - 17
After solving the equation, we find that x = 9.
b) To determine the measure of angle ZAXB, substitute x into the expression 5x + 10:
mZAXB = 5(9) + 10 = 55°
c) To calculate the measure of angle BXC, substitute x into the expression 8x – 17:
mZBXC = 8(9) - 17 = 55°
d) Since the measures of angles ZAXB and ZBXC are equal and sum up to 110°, the type of angle formed by XB and ZAXC is acute as each angle is less than 90°.