Answer:
[tex]<BOC = 42[/tex]
Step-by-step explanation:
In this problem, it is given that lines (AO) and (OC) are perpendicular. This means that when the lines intersect, the four angles formed each have a measure of (90) degrees. As per the given diagram, angles (<AOR) and (<ROC) add up to make (<AOC). Thus, one can form the following equation and solve for (x).
[tex](<AOR) + (<ROC) = (<AOC)[/tex]
Substitute,
[tex](6x-6)+(5x+8)=90[/tex]
Simplify,
[tex]11x+2=90[/tex]
Inverse operations,
[tex]11x+2=90[/tex]
[tex]11x=88\\\\x=8[/tex]
Substitute this into the equation for the measure of angle (<BOC) to find the numerical angle measure:
[tex]<BOC = 6x-6\\x = 8\\\\= 6(8)-6\\\\=48-6\\\\=42[/tex]
