Question

in \\( \triangle hij, mathrm{m} angle h=(x - 12)^{circ}, mathrm{m} angle i=(x - 5)^{circ}, \\) and \\( mathrm{m} angle j=(9 x - 1)^{circ} \\). what is the value of \\( x \\)?

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x - 12)+(x - 5)+(9x - 1)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+x + 9x)+(-12-5 - 1)=180\), which gives \(11x-18 = 180\).

Step3: Solve for \(x\)

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

Answer:

\(x = 18\)