In the following figure, if AOB is a straight line then find the measures of $\angle AOC$ and $\angle BOC$.
"
Given :
AOB is a straight line.
$\angle AOC = 3x+20, \angle BOC = 4x-36$.
To do :
We have to find the values of $\angle AOC$ and $\angle BOC$.
Solution :
We know that,
The sum of the angles in a straight line is 180°.
This implies,
$(3x+20)°+(4x-36)° = 180°$
$3x+4x+20°-36°=180°$
$7x-16° = 180°$
$7x = 180°+16°$
$7x = 196°$
$x = \frac{196°}{7}$
$x = 28°$
Therefore,
$∠AOC = (3x+20)° = (3(28)+20)° = (84+20)° = 104°$
$∠BOC = (4x-36)° = (4(28)-36)° = (112-36)° = 76°$.
The measures of $∠AOC$ and $∠BOC$ are 104° and 76° respectively.
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