System of Equations: y= 14x & (I) x+y+90=180 & (II) Measures: 72^(∘) and 18^(∘)
Practice makes perfect
We want to find the measures of the non-right angles in a right triangle by creating a system of linear equations and solving it. Let's graph an example right triangle for this situation. Remember that a right angle has a measure of 90^(∘) . Let x and y represent the measures of the unknown acute angles.
We know that the measure of one of the acute angles y is one-fourth the measure of another acute angle x. Let's use this information to create the first equation.
y= 1/4 x
The measures of the interior angles in a triangle add up to 180^(∘).
Keeping this in mind, let's write down the second equation.
x+ y+ 90=180
Now, we can combine both equations and create the system of equations.
y= 14x & (I) x+y+90=180 & (II)
Next, we will solve this system using the Substitution Method. Notice that Equation (I) is already solved for y. Because of this, we can substitute 14x for y in Equation (II) and solve it for x. Let's do it!
Finally, we will substitute 72 for x in Equation (I) and solve it for y. Keep in mind that, after finding the value of one of the variables, we can substitute it into either equation. We chose Equation (I) for because it is easier.
