Question

1. find m∠ljk if m∠ijl = 23°, m∠ijk = 55x - 2, and m∠ljk = 47x - 1. a) 140° b) 93° c) 95° d) 103°

Explanation:

Step1: Use angle - addition postulate

We know that \(m\angle IJK=m\angle IJL + m\angle LJK\). Substitute the given angle - measures: \(55x−2=23+(47x - 1)\).

Step2: Simplify the right - hand side of the equation

\(55x−2=23 + 47x-1\), which simplifies to \(55x−2=47x + 22\).

Step3: Solve for \(x\)

Subtract \(47x\) from both sides: \(55x-47x−2=47x-47x + 22\), so \(8x−2=22\). Then add 2 to both sides: \(8x-2 + 2=22 + 2\), getting \(8x=24\). Divide both sides by 8: \(x = 3\).

Step4: Find \(m\angle LJK\)

Substitute \(x = 3\) into the expression for \(m\angle LJK\). \(m\angle LJK=47x−1\), so \(m\angle LJK=47\times3−1=141 - 1=140^{\circ}\).

Answer:

A. \(140^{\circ}\)