Question

find the value of x. then find the measure of each angle and write the answers in ascending order.
x =

Explanation:

Step1: Use the triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). In a right - triangle (one angle is \(90^{\circ}\)), we have \(x + 2x+90=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \(3x+90 = 180\).
Subtract \(90\) from both sides: \(3x=180 - 90\), so \(3x = 90\).
Divide both sides by \(3\): \(x=\frac{90}{3}=30\).

Step3: Find the measure of each angle

When \(x = 30\), one angle is \(x^{\circ}=30^{\circ}\), another angle is \(2x^{\circ}=2\times30 = 60^{\circ}\), and the right - angle is \(90^{\circ}\).

Answer:

\(x = 30\); \(30^{\circ}\), \(60^{\circ}\), \(90^{\circ}\)