Question

1. one acute angle of a right triangle is 36° more than twice the other angle. which of the following systems of equations could be used to find the smaller angle?

○ x = y + 36
x + y = 90
○ x = 2y + 36
x + y = 90
○ x + 36 = 2y
x + y = 90
○ x = 2y + 36
x + y = 180

Explanation:

Step1: Define the relationship between the angles

Let \(x\) and \(y\) be the two acute - angles of the right - triangle. Given that one acute angle is 36 more than twice the other angle. If we assume \(x\) is the larger angle and \(y\) is the smaller angle, then \(x = 2y+36\).

Step2: Use the angle - sum property of a right - triangle

The sum of the two acute angles in a right - triangle is 90 degrees. So, \(x + y=90\).

Answer:

\(x = 2y + 36\), \(x + y = 90\) (the second option in the original multiple - choice list)