# The measure of the supplement of an angle is 40^{circ} more than three times the measure of the original angle.

The measure of the supplement of an angle is ${40}^{\circ }$ more than three times the measure of the original angle. Find the measure of the angles. Instructions: Use the statement: " Let the original angle be x " to begin modeling the working of this question.

a) Write algebraic expression in terms of x for the following:

I) ${40}^{\circ }$ more than three times the measure of the original angle

II) The measure of the Supplement angle in terms of the original angle, x

b) Write an algebraic equation in x equating I) and II) in a)

c) Hence solve the algebraic equation in

b) and find the measure of the angles.

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Willie

Let the original angle be x. The supplement of the angle is given as

a)

I) ${40}^{\circ }$ more than three times the measure of the original angle $={40}^{\circ }+3x$

II) The measure of the Supplement angle in terms of the original angle, x $=180-x$

b) Write an algebraic equation in x equating I) and II) in a) $180-x={40}^{\circ }+3x$

c) Hence solve the algebraic equation in  b) and find the measure of the angles.

$180-x={40}^{\circ }+3x$
$180-40=3x+x$
$4x=140$
$x={15}^{\circ }$