Question

adv geometry chapter 1 review
1 if the angle is acute what are the restrictions for x?
2x + 20

Explanation:

Step1: Recall definition of acute angle

An acute - angle has a measure between 0 and 90 degrees. So, we set up the inequality \(0<2x + 20<90\).

Step2: Solve the left - hand side of the inequality

Solve \(0<2x + 20\). Subtract 20 from both sides: \(0-20<2x+20 - 20\), which simplifies to \(- 20<2x\). Then divide both sides by 2: \(\frac{-20}{2}<\frac{2x}{2}\), giving \(-10 < x\).

Step3: Solve the right - hand side of the inequality

Solve \(2x + 20<90\). Subtract 20 from both sides: \(2x+20 - 20<90 - 20\), which simplifies to \(2x<70\). Then divide both sides by 2: \(\frac{2x}{2}<\frac{70}{2}\), giving \(x < 35\).

Answer:

\(-10 < x<35\)