Question

1. (mangle zhg = 11x - 1), (mangle ihz = 24^{circ}), and (mangle ihg = 12x + 13). find (mangle ihg).

Explanation:

Step1: Use angle - addition postulate

We know that \(m\angle IHG=m\angle IHZ + m\angle ZHG\). So, \(12x + 13=24+(11x - 1)\).

Step2: Simplify the right - hand side of the equation

Simplify \(24+(11x - 1)\) to get \(11x+23\). So the equation becomes \(12x + 13=11x + 23\).

Step3: Solve for \(x\)

Subtract \(11x\) from both sides: \(12x-11x+13=11x - 11x+23\), which gives \(x + 13=23\). Then subtract 13 from both sides: \(x=23 - 13=10\).

Step4: Find \(m\angle IHG\)

Substitute \(x = 10\) into the expression for \(m\angle IHG\). \(m\angle IHG=12x + 13\), so \(m\angle IHG=12\times10+13=120 + 13=133^{\circ}\).

Answer:

\(133^{\circ}\)