The measure of one angle is 2/3 the measure of another. The sum of the angles is 180 degrees....

Question:

The measure of one angle is {eq}\frac{2}{3} {/eq} the measure of another. The sum of the angles is 180 degrees. What are the measures of the angles?

Using Algebra to Solve Problems:

We can Algebra to solve many problems in our daily life. Here all we have to do is, we assume a variable for the unknown quantity, set an equation based upon the given conditions, apply algebraic operations on both sides of the equation and solve for the variable.

Answer and Explanation:

Let one angle be {eq}x {/eq}.

Then the other angle using the given information is: {eq}\dfrac{2x}{3} {/eq}.

The sum of these two angles is given to be 180 degrees. So we get:

$$\begin{align} x+\dfrac{2x}{3} &=180 \\ \dfrac{3x}{3}+ \dfrac{2x}{3}&=180 & \text{(Deonominators are made same)} \\ \dfrac{5x}{3}&=180 & \text{(Fractions are added)} \\ 5x &= 540 & \text{(Multiplied both sides by 3)} \\ x &=108 & \text{(Divided both sides by 5)} \end{align} $$

So one angle is 108 degrees.

The other angle is: {eq}\dfrac{2x}{3} = \dfrac{2 \times 108}{3}=72 {/eq}.

Therefore, the required angles are {eq}\boxed{\mathbf{108}} {/eq} degrees and {eq}\boxed{\mathbf{72}} {/eq} degrees.