Question

1. find x and m∠a. (9x + 17)° a (3x - 4)° b (6x - 31)° c x = __ m∠a = __

Explanation:

Step1: Apply 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: Isolate the variable \(x\)

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

Step4: Find \(m\angle A\)

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

Answer:

\(x = 11\)
\(m\angle A=116\)