Question

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

Modeling data distributions
ANSWERED
asked 2021-02-02

The measure of the supplement of an angle is \(\displaystyle{40}^{{\circ}}\) 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.

Answers (1)

2021-02-03

Let the original angle be x. The supplement of the angle is given as \(\displaystyle{180}\ -\ {x}.\)

a)

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

II) The measure of the Supplement angle in terms of the original angle, x \(\displaystyle={180}-{x}\)

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

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

\(\displaystyle{180}-{x}={40}^{{\circ}}+{3}{x}\)
\(\displaystyle{180}-{40}={3}{x}+{x}\)
\(\displaystyle{4}{x}={140}\)
\(\displaystyle{x}={15}^{{\circ}}\)

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