Question

Need help with this problem

Answer 1

`<BOC = 42`

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).

`(<AOR) + (<ROC) = (<AOC)`

Substitute,

`(6x-6)+(5x+8)=90`

Simplify,

`11x+2=90`

Inverse operations,

`11x+2=90`

`11x=88\\\\x=8`

Substitute this into the equation for the measure of angle (<BOC) to find the numerical angle measure:

`<BOC = 6x-6\\x = 8\\\\= 6(8)-6\\\\=48-6\\\\=42`

Answer 2

OA⊥OC

∴∠AOB+BOC= 90°

5x+8+6n-6=90

11x+2=90

x=90-2/11

x=88/11

x=8

∠BOC=6x-6

=6(8)-6

=48-6

∠BOC=42°

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