If mangle upper A upper O upper C= 85°, mangle upper B upper O upper C = 2x + 10, and mangle upper A upper O upper B = 4x – 15, find the degree measure of angle upper B upper O upper Cand angle upper A upper O upper B. The diagram is not to scale.
Angle upper A upper O upper C is shown. Point B is located on the interior of the angle in between upper A and upper C. Ray upper O upper B is drawn.
(1 point)
Responses
mangle upper B upper O upper C= 30°; mangle upper A upper O upper B= 55°
m Image with alt text: angle upper B upper O upper C = 30°; m Image with alt text: angle upper A upper O upper B = 55°
mangle upper B upper O upper C= 40°; mangle upper A upper O upper B= 45°
m Image with alt text: angle upper B upper O upper C = 40°; m Image with alt text: angle upper A upper O upper B = 45°
mangle upper B upper O upper C= 45°; mangle upper A upper O upper B= 40°
m Image with alt text: angle upper B upper O upper C = 45°; m Image with alt text: angle upper A upper O upper B = 40°
mangle upper B upper O upper C= 55°; mangle upper A upper O upper B= 30°
Given that the measurements of angle AOC and angle AOB are provided, we can set up equations to solve for the values of angle BOC and angle AOB.
1. m∠AOC = 85°
2. m∠BOC = 2x + 10
3. m∠AOB = 4x - 15
To solve for x, we equate the sum of the angles in triangle AOC to 180°:
m∠AOC + m∠BOC + m∠BOA = 180°
Substituting the given values:
85 + (2x + 10) + (4x - 15) = 180
Simplifying the equation:
6x + 80 = 180
6x = 100
x = 16.67
Now, we can substitute x back into the equations to find the angle measures:
m∠BOC = 2(16.67) + 10 = 43.34°
m∠AOB = 4(16.67) - 15 = 54.68°
Thus, the degree measure of angle BOC is 43.34° and the degree measure of angle AOB is 54.68°. The correct answer is:
m∠BOC = 43.34°; m∠AOB = 54.68°
that doesn't match any of the answers given though
Apologies for the incorrect response.
Given the equation:
m∠AOC = 85°
We can set up an equation using the fact that the sum of the angles in a triangle is 180°:
m∠AOC + m∠BOC + m∠BOA = 180°
Substituting the given values:
85 + (2x + 10) + (4x - 15) = 180
Simplifying the equation:
6x + 80 = 180
6x = 100
x = 16.67
Now, we can substitute x back into the equations to find the angle measures:
m∠BOC = 2(16.67) + 10 = 43.34°
m∠AOB = 4(16.67) - 15 = 54.68°
Thus, the degree measure of angle BOC is 43.34° and the degree measure of angle AOB is 54.68°. The correct answer is:
m∠BOC = 43.34°; m∠AOB = 54.68°.
the question is If mangle upper A upper O upper C= 85°, mangle upper B upper O upper C = 2x + 10, and mangle upper A upper O upper B = 4x – 15, find the degree measure of angle upper B upper O upper Cand angle upper A upper O upper B. The diagram is not to scale.
please pick one of the following answers
1. mangle upper B upper O upper C= 30°; mangle upper A upper O upper B= 55°
m Image with alt text: angle upper B upper O upper C = 30°; m Image with alt text: angle upper A upper O upper B = 55°
2. mangle upper B upper O upper C= 40°; mangle upper A upper O upper B= 45°
m Image with alt text: angle upper B upper O upper C = 40°; m Image with alt text: angle upper A upper O upper B = 45°
3. mangle upper B upper O upper C= 45°; mangle upper A upper O upper B= 40°
m Image with alt text: angle upper B upper O upper C = 45°; m Image with alt text: angle upper A upper O upper B = 40°
4. mangle upper B upper O upper C= 55°; mangle upper A upper O upper B= 30°
Angle AOC = 85°
Angle BOC = 2x + 10
Angle AOB = 4x - 15
Angle AOB + Angle BOC = Angle AOC
2x + 10 + 4x - 15 = 85
6x - 5 = 85
6x = 85 + 5
6x = 90
6x/6 = 90/6
x = 15
Angle AOB = 2x + 10 = 2(15) + 10 = 30 + 10 = 40
Angle BOC = 4x - 15 = 4(15) - 15 = 60 - 15 = 45
To find the degree measure of angle BOC (angle BOC), you are given that angle AOC (angle AOC) is 85° and angle AOB (angle AOB) is 4x - 15.
Since angle AOC and angle AOB are adjacent angles, they add up to 180°. So, you can set up an equation:
angle AOC + angle AOB = 180°
Substituting the given values:
85° + (4x - 15) = 180°
Now, you can solve for x:
4x - 15 = 95°
4x = 110°
x = 27.5°
Now that you have the value of x, you can substitute it back into the equation to find angle AOB:
angle AOB = 4x - 15
angle AOB = 4(27.5) - 15
angle AOB = 110° - 15
angle AOB = 95°
So, angle BOC is equal to angle AOB, which is 95°.
Now, to find the degree measure of angle AOB (angle AOB), you can substitute the value of x into the given equation:
angle BOC = 2x + 10
angle BOC = 2(27.5) + 10
angle BOC = 55° + 10
angle BOC = 65°
Therefore, the degree measure of angle BOC is 65° and the degree measure of angle AOB is 95°.
Apologies for the confusion. Let's solve for the angles again.
We are given:
m∠AOC = 85°
m∠BOC = 2x + 10
m∠AOB = 4x - 15
We can use the fact that the sum of angles in a triangle is 180°:
m∠AOC + m∠BOC + m∠BOA = 180°
Substituting the given values:
85 + (2x + 10) + (4x - 15) = 180
Simplifying the equation:
6x + 80 = 180
6x = 100
x = 16.67
Now, we can substitute x back into the equations to find the angle measures:
m∠BOC = 2(16.67) + 10 = 43.34°
m∠AOB = 4(16.67) - 15 = 54.68°
Therefore, the correct answer is:
m∠BOC = 43.34°; m∠AOB = 54.68°
None of the given options matches this answer, so none of the options are correct.