Lines AC and BD intersect at point O.If m∠AOD = (10x − 7)° and m∠BOC = (7x + 11)°, what is m∠BOC?Group of answer choices53°89°6°106°

Question

Lines AC and BD intersect at point O.

If
m∠AOD = (10x − 7)°
and
m∠BOC = (7x + 11)°,

what is m∠BOC?
Group of answer choices
53°
89°
6°
106°

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Solution

To find the measure of ∠BOC, we first need to understand that lines AC and BD intersect at point O, forming vertical angles ∠AOD and ∠BOC. Vertical angles are always equal.

So, we can set the measures of these angles equal to each other and solve for x:

10x - 7 = 7x + 11

Subtract 7x from both sides:

3x - 7 = 11

Add 7 to both sides:

3x = 18

Divide by 3:

x = 6

Now that we know x = 6, we can substitute it back into the equation for m∠BOC:

m∠BOC = 7x + 11 = 7(6) + 11 = 42 + 11 = 53°

So, the measure of ∠BOC is 53°.

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Lines AC and BD intersect at point O.If m∠AOD = (10x − 7)° and m∠BOC = (7x + 11)°, what is m∠BOC?Group of answer choices53°89°6°106°

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