Question

use the given information.
if ( mangle zhg = 11x - 1 ), ( mangle ihz = 24^{circ} ), and ( mangle ihg = 12x + 13 ), what is the ( mangle ihg )?
a ( 133^{circ} )
b ( 10^{circ} )
c ( 156^{circ} )
d ( 109^{circ} )

Explanation:

Step1: Use angle - addition postulate

By the angle - addition postulate, \(m\angle ZHG=m\angle IHZ + m\angle IHG\).
Substitute the given expressions: \(11x - 1=24+(12x + 13)\).

Step2: Solve the equation for \(x\)

Simplify the right - hand side: \(11x - 1=12x+37\).
Subtract \(11x\) from both sides: \(-1=x + 37\).
Subtract 37 from both sides: \(x=-38\).

Step3: Find \(m\angle IHG\)

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

Answer:

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