Equation practice with angle addition
Given:
m∠AOCm, angle, A, O, C is a straight angle.
\qquad m \angle BOC = 6x + 29^\circm∠BOC=6x+29
∘
m, angle, B, O, C, equals, 6, x, plus, 29, degrees
\qquad m \angle AOB = 3x + 124^\circm∠AOB=3x+124
∘
Find m\angle BOCm∠BOCm, angle, B, O, C:
B
_____________/_______________C
O
m∠AOCm, angle, A, O, C is a straight angle.
\qquad m \angle BOC = 6x + 29^\circm∠BOC=6x+29
∘
m, angle, B, O, C, equals, 6, x, plus, 29, degrees
\qquad m \angle AOB = 3x + 124^\circm∠AOB=3x+124
∘
m, angle, A, O, B, equals, 3, x, plus, 124, degrees
Find m\angle BOCm∠BOCm, angle, B, O, C:
since AOC is a straight line,
AOB+BOC = 180°
Thus,
3x+124 + 6x+29 = 180
9x + 153 = 180
9x = 27
x = 3
BOC = 6x+29 = 47°
m∠BOC=47
i need help
To find the measure of angle BOC, we can use the angle addition postulate.
The angle addition postulate states that if angle AOC is a straight angle, then the sum of angle AOB and angle BOC will be equal to angle AOC.
So, we can set up an equation using this postulate:
m∠AOB + m∠BOC = m∠AOC
Substituting the given measures:
(3x + 124) + (6x + 29) = 180
Simplifying the equation:
9x + 153 = 180
Now, we can solve this equation for x:
9x = 180 - 153
9x = 27
Divide both sides by 9:
x = 3
Now that we have found the value of x, we can substitute it back into the equation to find the measure of angle BOC:
m∠BOC = 6x + 29
m∠BOC = 6(3) + 29
m∠BOC = 18 + 29
m∠BOC = 47 degrees
Therefore, the measure of angle BOC is 47 degrees.