Question

1. find the value of x and m∠a.

(9x + 17)°
(3x - 4)°
(6x - 31)°

Explanation:

Step1: Use the triangle angle - sum theorem

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

Step2: Simplify the left - hand side of the equation

Combine like terms: \((3x+9x + 6x)+(-4 + 17-31)=180\).
\(18x-18 = 180\).

Step3: Solve for \(x\)

Add \(18\) to both sides: \(18x=180 + 18\), \(18x=198\).
Divide both sides by \(18\): \(x=\frac{198}{18}=11\).

Step4: Find \(m\angle A\)

Substitute \(x = 11\) into the expression for \(\angle A\): \(m\angle A=(9x + 17)\).
\(m\angle A=9\times11+17\).
\(m\angle A=99 + 17=116^{\circ}\).

Answer:

\(x = 11\) and \(m\angle A=116^{\circ}\)