Answer & Step-by-step explanation:
AOC is a straight angle. Straight angles have a measurement of 180°. ∠AOB and ∠BOC make up ∠AOC. So this measn that when you add ∠AOB to ∠BOC, then they should have a sum of 180°.
<em>m∠AOB + m∠BOC = 180°</em>
<em>m∠AOB = 3x + 142</em>
<em>m∠BOC = 6x + 29</em>
Now, set up the equation.
<em>3x + 142 + 6x + 29 = 180</em>
<em>9x + 171 = 180</em>
<em>9x = 9</em>
<em>x = 1</em>
Now that we have the value of x, then we can find the measurement of ∠BOC.
m∠BOC = 6(1) + 29
m∠BOC = 35
So, the measurement of ∠BOC is 35°
