Question

m∠cod = 9x + 4, m∠boc = 4x - 1, m∠bod = 14x - 6

Explanation:

Step1: Use angle - addition property

Since $\angle BOD=\angle BOC + \angle COD$, we can set up the equation $(4x - 1)+(9x + 4)=14x-6$.

Step2: Combine like - terms on the left - hand side

$4x+9x-1 + 4=14x-6$, which simplifies to $13x + 3=14x-6$.

Step3: Solve for x

Subtract $13x$ from both sides: $3=x - 6$. Then add 6 to both sides to get $x = 9$.

Step4: Find $m\angle BOD$

Substitute $x = 9$ into the expression for $m\angle BOD$: $m\angle BOD=14x-6=14\times9-6=126 - 6=120$.

Step5: Find $m\angle COD$

Substitute $x = 9$ into the expression for $m\angle COD$: $m\angle COD=9x + 4=9\times9+4=81 + 4=85$.

Step6: Find $m\angle BOC$

Substitute $x = 9$ into the expression for $m\angle BOC$: $m\angle BOC=4x-1=4\times9-1=36 - 1=35$.

Answer:

$x = 9$
$m\angle BOD=120$
$m\angle COD=85$
$m\angle BOC=35$