Question

extra practice level up your skills! find the measure of ∠acb. a (2x + 2)° (5x − 10)° (2x + 2)° b d c m∠acb = ______°

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle \(ABC\), \(\angle ACD\) is an exterior angle, so \(\angle ACD=\angle CAB+\angle CBA\).

We know that \(\angle ACD=(5x - 10)^{\circ}\), \(\angle CAB=(2x + 2)^{\circ}\) and \(\angle CBA=(2x + 2)^{\circ}\). So we can set up the equation:
\(5x-10=(2x + 2)+(2x + 2)\)

Step2: Solve the equation for x

Simplify the right - hand side of the equation:
\(5x-10=4x + 4\)

Subtract \(4x\) from both sides:
\(5x-4x-10=4x-4x + 4\)
\(x-10 = 4\)

Add 10 to both sides:
\(x-10 + 10=4 + 10\)
\(x=14\)

Step3: Find the measure of \(\angle ACB\)

We know that \(\angle ACD\) and \(\angle ACB\) are supplementary (they form a linear pair), so \(\angle ACB + \angle ACD=180^{\circ}\), which means \(\angle ACB=180^{\circ}-\angle ACD\).

First, find the measure of \(\angle ACD\): substitute \(x = 14\) into \(\angle ACD=(5x-10)^{\circ}\)
\(\angle ACD=5\times14-10=70 - 10=60^{\circ}\)

Then, find \(\angle ACB\):
\(\angle ACB=180^{\circ}-60^{\circ}=120^{\circ}\)

Answer:

\(120\)