Question

for questions 7 and 8, find the measure of ∠a. m∠a =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \((3x - 4)+(9x + 17)+(6x-31)=180\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \((3x+9x + 6x)+(-4 + 17-31)=180\), which simplifies to \(18x-18 = 180\).

Step3: Solve for \(x\)

Add 18 to both sides of the equation: \(18x-18 + 18=180 + 18\), giving \(18x=198\). Then divide both sides by 18: \(x=\frac{198}{18}=11\).

Step4: Find the measure of \(\angle A\)

Substitute \(x = 11\) into the expression for \(\angle A\), which is \(9x + 17\). So, \(m\angle A=9\times11 + 17=99+17 = 116\).

Answer:

116°