Question

problem 19: (first taught in lesson 15) an angle is equal to one - third its complement. find the angles measure. after you enter your answer press go.

Explanation:

Step1: Define the angle and its complement

Let the angle be $x$. Its complement is $90 - x$.

Step2: Set up the equation

Given $x=\frac{1}{3}(90 - x)$.

Step3: Solve the equation

Expand: $x = 30-\frac{1}{3}x$.
Add $\frac{1}{3}x$ to both sides: $x+\frac{1}{3}x=30$.
Combine like - terms: $\frac{3x + x}{3}=30$, so $\frac{4x}{3}=30$.
Multiply both sides by $\frac{3}{4}$: $x = 30\times\frac{3}{4}=\frac{90}{4}=22.5^{\circ}$.

Answer:

$22.5^{\circ}$