Question

use the given information. if m∠zhg = 11x - 1, m∠ihz = 24°, and m∠ihg = 12x + 13, what is the m∠ihg? a 133° b 10° c 156° d 109°

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: Solve the equation for \(x\)

Simplify the right - hand side of the equation: \(12x + 13=24 + 11x-1\), which becomes \(12x + 13=11x + 23\). Subtract \(11x\) from both sides: \(12x-11x+13=11x-11x + 23\), so \(x+13 = 23\). Then subtract 13 from both sides: \(x=23 - 13=10\).

Step3: Find \(m\angle IHG\)

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

Answer:

A. \(133^{\circ}\)