"If m= Angle AOC=49°, m=Angle BOC = 2x + 10, and m Angle AOB = 4x – 15, find the degree measure of Angle BOCand Angle AOB. The diagram is not to scale.
To find the degree measure of Angle BOC, we can set up an equation using the given information. We know that m Angle BOC = 2x + 10. Since Angle AOC is 49°, we can set up the equation:
Angle BOC = Angle AOC
2x + 10 = 49
Solving this equation, we find:
2x = 39
x = 39/2
x = 19.5
Now, we can substitute this value back into the equation for Angle BOC:
Angle BOC = 2(19.5) + 10
Angle BOC = 39 + 10
Angle BOC = 49
Therefore, the degree measure of Angle BOC is 49°.
To find the degree measure of Angle AOB, we can use the information that m Angle AOB = 4x – 15. Substitute the value of x we found earlier:
Angle AOB = 4(19.5) – 15
Angle AOB = 78 – 15
Angle AOB = 63
Therefore, the degree measure of Angle AOB is 63°.
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Saludos cordiales
Buenas tardes,
Muchas gracias por responder a mi correo electrónico. Ahora sí me llegó el mensaje. Espero que pronto se pueda resolver mi problema. En el futuro, me pondré nuevamente en contacto con ustedes. ¡Que tenga un buen día!
Saludos cordiales
To find the degree measure of angle BOC and angle AOB, we need to equate the angles and solve for x.
Given:
Angle AOC = 49°
Angle BOC = 2x + 10
Angle AOB = 4x - 15
Since angle BOC is the same as angle AOC, we can equate them:
Angle AOC = Angle BOC
49° = 2x + 10
Now we can solve this equation for x:
49° - 10 = 2x
39° = 2x
x = 39° / 2
x = 19.5°
Now, substitute the value of x into the equation for angle AOB:
Angle AOB = 4x - 15
Angle AOB = 4(19.5°) - 15
Angle AOB = 78° - 15
Angle AOB = 63°
Therefore, the degree measure of Angle BOC is 49°, and the degree measure of Angle AOB is 63°.