Question

1. (l30) find the measures of the angles of a right triangle whose acute angles have measures of 5x and 4x.
2. (l30) find the measures of the angles of a triangle whose angles have measures of x - 20, 3x,

and 4x.
a. 35, 55, 90
b. 5, 40, 65
c. 15, 25, 45
d. 5, 75, 100
e. none of the above

1. (l28) a polygon is a geometric figure whose sides are —

a. lines

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). For a right - triangle, one angle is \(90^{\circ}\). Let the acute angles be \(5x\) and \(4x\). Then \(5x + 4x+90^{\circ}=180^{\circ}\).

Step2: Solve the equation for \(x\)

Combine like terms: \(9x+90 = 180\). Subtract \(90\) from both sides: \(9x=180 - 90\), so \(9x = 90\). Divide both sides by \(9\): \(x = 10\).

Step3: Find the measures of \(5x\) and \(4x\)

If \(x = 10\), then \(5x=5\times10 = 50\) and \(4x = 4\times10=40\).

Answer:

A. \(40,50,90\)