Question

using tools. find the value of k. then find the angle measures of the polygon. sum of angle measures: 180°. 45° 2k° k°

Explanation:

Step1: Set up equation using angle - sum property

The sum of the interior angles of a triangle is 180°. So, \(k + 2k+45=180\).

Step2: Combine like - terms

Combining the \(k\) terms, we get \(3k + 45=180\).

Step3: Isolate the variable term

Subtract 45 from both sides: \(3k=180 - 45\), so \(3k = 135\).

Step4: Solve for \(k\)

Divide both sides by 3: \(k=\frac{135}{3}=45\).

Step5: Find the angle measures

The angles are: \(k = 45^{\circ}\), \(2k=2\times45 = 90^{\circ}\), and the given angle is \(45^{\circ}\).

Answer:

\(k = 45\), and the angle measures are \(45^{\circ},90^{\circ},45^{\circ}\)