If mangle upper A upper O upper C = 49°, 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 C and 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 = 21°; mangle upper A upper O upper B = 28°
m Image with alt text: angle upper B upper O upper C = 21°; m Image with alt text: angle upper A upper O upper B = 28°
mangle upper B upper O upper C = 18°; mangle upper A upper O upper B = 31°
m Image with alt text: angle upper B upper O upper C = 18°; m Image with alt text: angle upper A upper O upper B = 31°
mangle upper B upper O upper C = 28°; mangle upper A upper O upper B = 21°
m Image with alt text: angle upper B upper O upper C = 28°; m Image with alt text: angle upper A upper O upper B = 21°
mangle upper B upper O upper C = 31°; mangle upper A upper O upper B = 18°
m Image with alt text: angle upper B upper O upper C = 31°; m Image with alt text: angle upper A upper O upper B = 18°
To find angle upper B upper O upper C, we know that the sum of all angles in a triangle is 180°.
So, mangle upper A upper O upper C + mangle upper B upper O upper C + mangle upper A upper O upper B = 180°.
We are given that mangle upper A upper O upper C = 49° and mangle upper A upper O upper B = 4x - 15.
Substituting these values, we have:
49° + mangle upper B upper O upper C + (4x - 15°) = 180°
Simplifying the equation:
mangle upper B upper O upper C + 4x + 34° = 180°
Subtracting 34° from both sides:
mangle upper B upper O upper C + 4x = 146°
To find the value of x, we are also given mangle upper B upper O upper C = 2x + 10.
Substituting this value, we have:
2x + 10 + 4x = 146°
Combining like terms:
6x + 10 = 146°
Subtracting 10 from both sides:
6x = 136°
Dividing both sides by 6:
x = 22.67°
Now, substituting the value of x back into mangle upper B upper O upper C = 2x + 10:
mangle upper B upper O upper C = 2(22.67°) + 10 = 45.34 + 10 = 55.34°
Therefore, the degree measure of angle upper B upper O upper C is 55.34°.
Similarly, substituting the value of x into mangle upper A upper O upper B = 4x - 15:
mangle upper A upper O upper B = 4(22.67°) - 15 = 90.68 - 15 = 75.68°
Therefore, the degree measure of angle upper A upper O upper B is 75.68°.
The degree measures of angle upper B upper O upper C and angle upper A upper O upper B are:
mangle upper B upper O upper C = 55.34°; mangle upper A upper O upper B = 75.68°