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Answer: b.13
Explanation:
We have that P lies in the interior of the angle ABC, we can represent that as follows:
Where we have the angle ABC and P is in the interior of that angle.
Now, we are told that ABP = 3x+7, and PBC =x+3. We can represent this as follows:
And also, the whole angle ABC has a measure of: ABC = 6x-10
So the sum of the two angles in the image, must be equal to 6x-10:
[tex]\begin{gathered} \text{ABC}=\text{ABP}+\text{PBC} \\ 6x-10=3x+7+x+3 \end{gathered}[/tex]And we solve this equation for x combining like terms:
[tex]6x-10=4x+10[/tex]we add 10 to both sides of the equation:
[tex]\begin{gathered} 6x-10+10=4x+10+10 \\ 6x=4x+20 \\ 6x-4x=20 \\ 2x=20 \end{gathered}[/tex]And divide both sides by 2:
[tex]\begin{gathered} x=\frac{20}{2} \\ x=10 \end{gathered}[/tex]Now that we have the value of x, we can find the value of PBC which is x+3:
[tex]PBC=x+3=10+3=13[/tex]Answer: b.13
