Question

ii. find the value of x for each. then find the measure of angle each missing angle. 8) 9) (5x - 5)° (3x)° (4x + 30)° 56°

Explanation:

8)

Step1: Use triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). So, \(90^{\circ}+40^{\circ}+3x = 180^{\circ}\)

Step2: Simplify the equation

\(130^{\circ}+3x=180^{\circ}\). Subtract \(130^{\circ}\) from both sides: \(3x=180 - 130\), \(3x = 50\)

Step3: Solve for \(x\)

Divide both sides by 3: \(x=\frac{50}{3}\approx16.67\)

Step4: Find the measure of the angle \((3x)^{\circ}\)

Substitute \(x = \frac{50}{3}\) into \(3x\). \(3\times\frac{50}{3}=50^{\circ}\)

Step1: Use triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). So, \((5x - 5)+(4x + 30)+56=180\)

Step2: Combine like terms

\((5x+4x)+(- 5 + 30+56)=180\), \(9x+(81)=180\)

Step3: Solve for \(x\)

Subtract 81 from both sides: \(9x=180 - 81\), \(9x = 99\). Divide both sides by 9: \(x = 11\)

Step4: Find the measure of \((5x - 5)^{\circ}\)

Substitute \(x = 11\) into \(5x-5\). \(5\times11-5=55 - 5=50^{\circ}\)

Step5: Find the measure of \((4x + 30)^{\circ}\)

Substitute \(x = 11\) into \(4x + 30\). \(4\times11+30=44+30=74^{\circ}\)

Answer:

\(x=\frac{50}{3}\), the missing angle is \(50^{\circ}\)

9)