In the above figure m AOC=21 and m BOD=(2x+39) degree if AIC and BOD are vertical angles what is the value of x
Since AIC and BOD are vertical angles, they are congruent. Therefore, m(AIC) = m(BOD).
m(AOC) + m(AIC) + m(COA) = 180°
21° + m(AIC) + m(COA) = 180°
m(AIC) + m(COA) = 180° - 21°
m(AIC) + m(COA) = 159°
m(BOD) + m(BDO) + m(DOB) = 180°
(2x + 39)° + m(DOB) + (2x + 39)° = 180°
4x + 78 + m(DOB) = 180°
4x + m(DOB) = 180° - 78
4x + m(DOB) = 102°
Since AIC and COA are vertical angles, they are congruent. Therefore, m(AIC) = m(COA).
Since BOD and BDO are vertical angles, they are congruent. Therefore, m(BOD) = m(DOB).
We can set up an equation using these two equations:
m(AIC) + m(COA) = m(BOD) + m(DOB)
159° = 4x + 102°
Subtract 102° from both sides:
159° - 102° = 4x
57° = 4x
Divide both sides by 4:
57°/4 = x
14.25° = x
So, the value of x is 14.25.