Introduce a variable for the measure of the smaller acute angle.
Smaller angle: 23^(∘) Larger angle: 67^(∘)
Practice makes perfect
The exercise reads like a riddle. We will break it down into steps. First, Let's introduce a variable x for the measure of the smaller acute angle.
We can then use the information given to write an expression for the measure of the larger acute angle in terms of this variable x.
Information
Expression
This is the variable we chose to be the measure of the smaller acute angle.
x
The measure of the larger acute angle is two degrees less than three times the measure of the smaller acute angle x.
3x - 2
Additionally, it is given that these are acute angles of a right triangle.
According to Corollary 4.1 of the Triangle Angle-Sum Theorem, the acute angles of a right triangle are complementary, so their measures add to 90^(∘).
We can use this to set up and solve an equation for x.
