The measure of an angle is 3 times the measure of its supplement. Find the measure of the angle.

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- Sep 17th 2008, 09:15 PMMary DannaGeometry angles
The measure of an angle is 3 times the measure of its supplement. Find the measure of the angle.

- Sep 17th 2008, 10:00 PMo_O
Let $\displaystyle {\color{red}s}$ be the supplement of the angle that we are looking at (which we'll call $\displaystyle \alpha$).

So, by definition, we know that: $\displaystyle \alpha + {\color{red}s} = 180^{\circ}$ (1)

We also know that the angle is 3 times more than its supplementary angle, i.e.: $\displaystyle \alpha = 3{\color{red}s} \ \ \text{which is the same as: } {\color{red}s} = \frac{\alpha}{3}$

So substitute $\displaystyle {\color{red}s}$ into (1) and we get: $\displaystyle \alpha + {\color{red}\frac{\alpha}{3}} = 180^{\circ}$

Now just solve for the angle $\displaystyle \alpha$ - Sep 18th 2008, 05:32 AMMary Danna
Thank you so much! I've never taken Geometry and my daughter has a test tomorrow. You helped a lot!