What is the sum of the three angles of a triangle?
18^(∘), 72^(∘)
Practice makes perfect
We are told that the measure of an acute angle in a right triangle is four times the measure of the other acute angle, and we are asked to find those measures. To do so, we will write and solve a System of Equations. If we call the first acute angle x and the second y, we can write this relationship as the following equation.
x=4y
We can use the fact that the triangle is a right triangle and that the sum of the three angles for any triangle is 180^(∘) to form our second equation.
x+y+90=180
Therefore, the system of equations can be written as follows.
x=4y & (I) x+y+90=180 & (II)
We will solve it using the Substitution Method. Since the x-variable is already isolated in Equation (I), we are going to substitute its equivalent expression in Equation (II).
We have found that x=72. Therefore, the solution of the system of equations, which is the point of intersection of the lines, is (18,72). That means that the measures of the acute angles are 18^(∘) and 72^(∘).
