Question

I'm stuck on this problem for like an hour I also need to show my work to get it right.

Answer 1

51 degrees

Step-by-step explanation:

Angle ABC is formed by a secant and a tangent.

`m\angle\text{ABC}=(1)/(2)(\text{m}\widehat{AD}-\widehat{AC}\text{)}`

Substitute the given values:

`\begin{gathered} 4x+15=(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=(18)/(2) \\ x=9 \end{gathered}`

Next, we find the measure of angle ABC.

`\begin{gathered} m\angle\text{ABC}=4x+15 \\ =4(9)+15 \\ =36+15 \\ m\angle\text{ABC}=51\degree \end{gathered}`