Question

find the value of k. then find the angle measures of the triangle. sum of angle measures: 180°. the angle measures are 15°, □, and □.

Explanation:

Step1: Set up angle - sum equation

We know that the sum of the interior angles of a triangle is 180°. So, \(42 + 3k + k=180\).
Combining like - terms, we get \(42 + 4k = 180\).

Step2: Solve for k

Subtract 42 from both sides of the equation: \(4k=180 - 42\).
\(4k = 138\).
Then divide both sides by 4: \(k=\frac{138}{4}=34.5\).

Step3: Find angle measures

One angle is \(42^{\circ}\).
Another angle is \(3k\), substituting \(k = 34.5\), we get \(3\times34.5=103.5^{\circ}\).
The third angle is \(k = 34.5^{\circ}\).

Answer:

\(k = 34.5\); The angle measures are \(42^{\circ}\), \(103.5^{\circ}\), and \(34.5^{\circ}\)