Question

Two angles are supplementary. The larger angle is 33 degrees more than 6 times the smaller angle. Find the measure of each angle.

Answer 1

Sum of two angles that are supplementary = 180°

Let the smaller angle be = x

$Let \: the \: smaller \: angle \: be \: = \: x$

$then \: the \: larger \: angle \: = 6x + 33$

Their sum :

$x + 6x + 33 = 180$

$7x + 33 = 180$

$7x = 180 - 33$

$7x = 147$

$x = \frac{147}{7}$

$x = 21$

Using this let us find the measures of the smaller angle and bigger angle .

$smaller \: angle \: = x = 21°$

$larger \: angle \: = 6x + 33 = 6 \times 21 + 33 = 126 + 33 = 159°$

∴ The measure of the two angles are = 21° and 159° .