Question

3)

x = ______

5)

x = ______
∠abc = ______
∠acb = ______

Explanation:

Problem 3:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). Given angles \(65^\circ\) and \(40^\circ\), let the third angle be \(x\).

Step2: Calculate \(x\)

\(x = 180^\circ - 65^\circ - 40^\circ\)
\(x = 75^\circ\)

Step1: Triangle angle sum

Sum of angles in \(\triangle ABC\) is \(180^\circ\). Angles: \(60^\circ\), \(3x\), \(3x\).

Step2: Solve for \(x\)

\(60 + 3x + 3x = 180\)
\(6x = 120\)
\(x = 20\)

Step3: Find \(\angle ABC\) and \(\angle ACB\)

\(\angle ABC = 3x = 3\times20 = 60^\circ\)
\(\angle ACB = 3x = 60^\circ\)

Answer:

\(75^\circ\)

Problem 5: