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 choices53°89°6°106°
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°.
Similar Questions
𝑁 is the point of intersection of the lines with equations 2𝑥−𝑦=−9 and 3𝑥+5𝑦=−7Write down the coordinates of 𝑁.
In the given figure, if ∠ABC = 20º, then∠AOC is equal to:(a) 20° (b) 40° (c) 12°(d) 10°
The adjoining figure is a rectangle whose diagonals AC and BD intersect at O. If ∠OAB = 27°, then find ∠OBC.
n Figure, if EC || AB, ∠∠ECD = 70° and ∠∠BDO = 20°, then ∠∠OBD is
D and E are points on the sides AB and AC respectively of a . If AB = 10.8 cm, AD = 6.3 cm, AC = 9.6cm, and EC = 4 cm. Determine whether or not.[2]△ABCDE∥BC
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.