Question

use the figure to answer the question. what is the value of y - x? a. 20 b. 30 c. 45 d. 60 e. 90

Explanation:

Step1: Use angle - sum property of right - angled triangle

The sum of angles in a right - angled triangle is 180°. In the right - angled triangle with angles \(x^{\circ}\), \(y^{\circ}\), and \(90^{\circ}\), we have \(x + y+90 = 180\), so \(x + y=90\). Also, from the figure, we can see that \(4x = 90\) (since the sum of the four non - right angles at the vertex is 90°).

Step2: Solve for \(x\)

Solve the equation \(4x = 90\) for \(x\). We get \(x=\frac{90}{4}=22.5\).

Step3: Solve for \(y\)

Substitute \(x = 22.5\) into \(x + y=90\). Then \(y=90 - x=90 - 22.5 = 67.5\).

Step4: Calculate \(y - x\)

Substitute the values of \(x\) and \(y\) into \(y - x\). \(y - x=67.5-22.5 = 45\).

Answer:

C. 45