Answer: [tex]x=13[/tex], one base angle measures [tex]74^{\circ}[/tex]
Step-by-step explanation:
The base angles of an isosceles triangle are congruent, so:
- 5x + 9 = 8x - 30 [congruent angles have equal measure]
- 9 = 3x - 30 [subtract 5x from both sides]
- 39 = 3x [add 30 to both sides]
- x = 13 [divide both sides by 3]
Hence, the measure of one base angle is [tex]5(13)+9=\boxed{74^{\circ}}[/tex]
