Answer:
51 degrees
Explanation:
Angle ABC is formed by a secant and a tangent.
[tex]m\angle\text{ABC}=\frac{1}{2}(\text{m}\widehat{AD}-\widehat{AC}\text{)}[/tex]
Substitute the given values:
[tex]\begin{gathered} 4x+15=\frac{1}{2}((\text{17x+2)}-(7x-10)\text{)} \\ 2(4x+15)=((\text{17x+2)}-(7x-10)\text{)} \\ 8x+30=17x+2-7x+10 \\ 8x+30=10x+12 \\ 30-12=10x-8x \\ 18=2x \\ x=\frac{18}{2} \\ x=9 \end{gathered}[/tex]
Next, we find the measure of angle ABC.
[tex]\begin{gathered} m\angle\text{ABC}=4x+15 \\ =4(9)+15 \\ =36+15 \\ m\angle\text{ABC}=51\degree \end{gathered}[/tex]
