# 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.

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.